62 Highway and Airport Pavement Design 62.1 Introduction 62.2 Pavement Types and Materials Flexible versus Rigid Pavement • Layered Structure of Flexible Pavement • Rigid Pavement • Considerations for Highway and Airport Pavements
62.3 Traffic-Loading Analysis for Highway Pavements Traffic Stream Composition • Traffic-Loading Computation • Directional Split • Design Lane Traffic Loading • Formula for Computing Total Design Loading
62.4 Traffic Loading Analysis for Airport Pavements Traffic Stream Composition • Computation of Traffic Loading • Equal Stress ESWL • Equal Deflection ESWL • Critical Areas for Pavement Design
62.5 Thickness Design of Flexible Pavements AASHTO Design Procedure for Flexible Highway Pavements • AI Design Procedure for Flexible Highway Pavements • FAA Design Procedure for Flexible Airport Pavements • Mechanistic Approach for Flexible Pavement Design
62.6 Structural Design of Rigid Pavements AASHTO Thickness Design for Rigid Highway Pavements • AASHTO Reinforcement Design for Rigid Highway Pavements • PCA Thickness Design Procedure for Rigid Highway Pavements • FAA Method for Rigid Airport Pavement Design
62.7 Pavement Overlay Design
T. F. Fwa National University of Singapore
AI Design Procedure for Flexible Overlay on Flexible Highway Pavement • AI Design Procedure for Flexible Overlay on Rigid Highway Pavement • PCA Design Procedure for Concrete Overlay on Concrete Highway Pavement • FAA Design Procedure for Flexible Overlay on Flexible Airport Pavement • FAA Design Procedure for Flexible Overlay on Concrete Airport Pavement • FAA Design Procedure for Concrete Overlay on Concrete Airport Pavement
62.1 Introduction Pavements are designed and constructed to provide durable all-weather traveling surfaces for safe and speedy movement of people and goods with an acceptable level of comfort to users. These functional requirements of pavements are achieved through careful considerations in the following aspects during the design and construction phases: (a) selection of pavement type, (b) selection of materials to be used for various pavement layers and treatment of subgrade soils, (c) structural thickness design for pavement
© 2003 by CRC Press LLC
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layers, (d) subsurface drainage design for the pavement system, (e) surface drainage and geometric design, and (f ) ridability of pavement surface. The two major considerations in the structural design of highway and airport pavements are material design and thickness design. Material design deals with the selection of suitable materials for various pavement layers and mix design of bituminous materials (for flexible pavement) or portland cement concrete (for rigid and interlocking block pavements). These topics are discussed in other chapters of this handbook. This chapter presents the concepts and methods of pavement thickness design. As the name implies, thickness design refers to the procedure of determining the required thickness for each pavement layer to provide a structurally sound pavement structure with satisfactory performance for the design traffic over the selected design life. Drainage design examines the entire pavement structure with respect to its drainage requirements and incorporates facilities to satisfy those requirements.
62.2 Pavement Types and Materials Flexible versus Rigid Pavement Traditionally, pavements are classified into two categories, namely flexible and rigid pavements. The basis for classification is the way by which traffic loads are transmitted to the subgrade soil through the pavement structure. As shown in Fig. 62.1, a flexible pavement provides sufficient thickness for load distribution through a multilayer structure so that the stresses and strains in the subgrade soil layers are within the required limits. It is expected that the strength of subgrade soil would have a direct bearing on the total thickness of the flexible pavement. The layered pavement structure is designed to take advantage of the decreasing magnitude of stresses with depth. A rigid pavement, by virtue of its rigidity, is able to effect a slab action to spread the wheel load over the entire slab area, as illustrated in Fig. 62.1. The structural capacity of the rigid pavement is largely provided by the slab itself. For the common range of subgrade soil strength, the required rigidity for a portland cement concrete slab (the most common form of rigid pavement construction) can be achieved (a) Typical Cross Section of Flexible Pavement
(b) Load Transmission in Flexible Pavement
Highway Airport Pavement Pavement Tack Coat Prime Coat
Wearing Course
1-2 in
Binder Course
2-4 in
Base Course
4-12 in
6-12 in
12-18 in
12-36 in
6-24 in
12-60 in
Subbase Course Prepared Subgrade Natural Subgrade
Wheel Load
3-6 in
(1 in = 25.4 mm)
(c) Typical Cross Section of Rigid Pavement
(d) Load Transmission in Rigid Pavement
Highway Airport Pavement Pavement Concrete Slab Base or Subbase Prepared Subgrade Natural Subgrade
FIGURE 62.1 Flexible and rigid pavements.
6-12 in
10-24 in
4-6 in
4-12 in
6-12 in
9-18 in
(1 in = 25.4 mm)
Wheel Load
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Highway and Airport Pavement Design
without much variation in slab thickness. The effect of subgrade soil properties on the thickness of rigid pavement is therefore much less important than in the case of flexible pavement.
Layered Structure of Flexible Pavement Surface Course In a typical conventional flexible pavement, known as asphalt pavement, the surface course usually consists of two bituminous layers — a wearing course and a binder course. To provide a durable, watertight, smooth-riding, and skid-resistant traveled surface, the wearing course is often constructed of dense-graded hot mix asphalt with polish-resistant aggregate. The binder course generally has larger aggregates and less asphalt. The composition of the bituminous mixtures and the nominal top size aggregates for the two courses are determined by the intended use, desired surface texture (for the case of wearing course), and layer thickness. A light application of tack coat of water-diluted asphalt emulsion may be used to enhance bonding between the two courses. Table 62.1 shows selected mix compositions listed in ASTM Standard Specification D3515 [1992]. Open-graded wearing courses, some with air void exceeding 20%, have also been used to improve skid resistance and reduce splash during heavy rainfall by acting as a surface drainage layer. Base Course Base and subbase layers of the flexible pavement make up a large proportion of the total pavement thickness needed to distribute the stresses imposed by traffic loading. Usually base course also serves as a drainage layer and provides protection against frost action. Crushed stone is the traditional material used for base construction to form what is commonly known as the macadam base course. In this construction, choking materials consisting of natural sand or the fine product resulting from crushing coarse aggregates are added to produce a denser structure with higher shearing resistance. Such base courses are called by different names, depending on the construction method adopted. Dry-bound macadam is compacted by means of rolling and vibration that work the choking materials into the voids of larger stones. For water-bound macadam, after spreading of the choking materials, water is applied before the entire mass is rolled. Alternatively, a wet-mix macadam may be used by premixing crushed stone or slag with a controlled amount of water. The material is spread by a paving machine TABLE 62.1
Example Composition of Dense Bituminous Paving Mixtures Mix Designation and Nominal Maximum Size of Aggregate
Sieve Size 2½ in. 2 in. 1½ in. 1 in. 3/4 in. 1/2 in. 3/8 in. No. 4 No. 8 No. 16 No. 30 No. 50 No. 100 No. 200
2 in. (50 mm)
1½ in. (37.5 mm)
1 in. (25.0 mm)
3/4 in. (19.0 mm)
1/2 in. (12.5 mm)
3/8 in. (9.5 mm)
100 90–100 — 60–80 — 35–65 — 17–47 10–36 — — 3–15 — 0–5
— 90–100 90–100 — 56–80 — — 23–53 15–41 — — 4–16 — 0–6
— 100 100 90–100 — 56–80 — 29–59 19–45 — — 5–17 — 1–7
— — — 100 90–100 — 56–80 35–65 23–49 — — 5–19 — 2–8
— — — — 100 90–100 — 44–74 28–58 — — 5–21 — 2–10
— — — — — 100 90–100 55–85 32–67 — — 7–23 — 2–10
Note: Numbers in table refer to percent passing by weight. Source: ASTM, Standard Specification D3515-84, Annual Book of ASTM Standards, Vol. 04.03 — Road and Paving Materials; Travelled Surface Characteristics, 1992. With permission.
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TABLE 62.2(a) Grading Requirements for Unbound Subbase and Base Materials — ASSHTO Designation M147-65 (1989) Grading: Percentage Passing Sieve Size 50 mm 25 mm 9.5 mm 4.75 mm 2 mm 425 mm 75 mm
A
B
C
D
E
F
100 — 30–60 25–55 15–40 8–20 2–8
100 75–95 40–75 30–60 20–45 15–30 5–20
100 50–85 35–65 25–50 15–30 5–15
100 60–100 50–85 40–70 25–45 5–20
100 — 55–100 40–100 20–50 6–20
100 — 70–100 55–100 30–70 8–25
Other requirements: 1. Coarse aggregate (>2 mm) to have a percentage wear by Los Angeles test not more than 50. 2. Fraction passing 425-mm sieve to have a liquid limit not greater than 25% and a plasticity index not greater than 6%. Source: AASHTO Designation M147-65, AASHTO Standard Specifications for Transportation Materials and Methods of Sampling and Testing, American Association of State Highway and Transportation Officials, Washington, D.C., 1989. With permission.
TABLE 62.2(b) ASTM Designation D2940-74 (Reapproved 1985) Grading: Percentage Passing Sieve Size
Bases
Subbases
50 mm 37.5 mm 19 mm 9.5 mm 4.75 mm 600 mm 75 mm
100 95–100 70–92 50–70 35–55 12–25 0–8
100 90–100 — — 30–60 — 0–12
Other requirements: 1. Fraction passing the 75-mm sieve not to exceed 60% of the fraction passing the 600-mm sieve. 2. Fraction passing the 425-mm sieve shall have a liquid limit not greater than 25% and a plasticity index not greater than 4%. Source: ASTM. 1992. ASTM Standard Specification D2940-74 (reapproved 1980), Annual Book of ASTM Standards. Vol. 04.03 — Road and Paving Materials; Travelled Surface Characteristics, 1992. With permission.
and compacted by a vibrating roller. Table 62.2 shows specifications for unbound base and subbase materials specified by AASHTO and ASTM. Granular base materials may be treated with either asphalt or cement to enhance load distribution capability. Bituminous binder can be introduced by spraying heated asphalt cement on consolidated and rolled crushed stone layer to form a penetration macadam road base. Alternatively, bituminous road bases can be designed and laid as in the case for bituminous surface courses. Cement-bound granular base material is plant mixed with an optimal moisture content for compaction. It is laid by paver and requires time for curing. Lean concrete base has also been used successfully under flexible pavements. Table 62.3 shows examples of grading requirements for these materials.
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TABLE 62.3
Requirements for Stabilized Base Courses Cement Treated
Specification
Class A
Class B
Bituminous Treated Class C
Class 1
Class 2
Lime Treated
(a) Stabilized Base Courses for Flexible Pavements Percent passing 2½ in. 3/4 in. No. 4 No. 10 No. 40 No. 200 7-day fc (psi) S (lb) F (0.01 in.) PI
100 — 65–100 20–45 15–30 5–12 650–1000 — — 12 max
100 — 55–100 — 25–50 5–20 300–650 — — —
100 75–95 25–60 15–45 8–30 2–15 — — —
750 min 16 max 6 max
500 min 20 max 6 max
— — 6 max
Specification
Type A (Open Graded)
Type B (Dense Graded)
Type C (Cement Graded)
Type D (Lime Treated)
Type E (Bituminous Treated)
Type F (Granular)
(b) Base Materials for Concrete Pavement Percent passing 1½ in. 3/4 in. No. 4 No. 40 No. 200
100 100 100 — — 60–90 85–100 — * * 35–60 50–80 65–100 — — 10–25 20–35 25–50 — — 0–7 5–12 5–20 — — (The minus No. 200 material should be held to a practical minimum) 28-day fc (psi) — — 400–750 100 — S (lb) — — — — 500 min F (0.01 in.) — — — — 20 max Soil constants: LL 25 max 25 max — — — PI* N.P. 6 max 10 max — 6 max
100 — 65–100 25–50 0–15 — — — 25 max 6 max
Notes: *
To be determined by complete laboratory analysis, taking into consideration the ability of the stabilized mixture to resist underslab erosion. fc = compressive strength as determined in unconfined compression tests on cylinders 4 inches in diameter and 4 inches high. Test specimens should contain the same percentage of portland cement and be compacted to the same density as achieved in construction. S = Marshall stability. F = Marshall flow. PI = plasticity index performed on samples prepared in accordance with AASHTO Designation T-87 and applied to aggregate prior to mixing with the stabilizing admixture, except that, in the case of lime-treated base, the value is applied after mixing. LL= liquid limit. Source: AASHTO Interim Guide for Design of Pavement Structures, American Association of State Highway and Transportation Officials, Washington, D.C., 1972. With permission.
Subbase Course The subbase material is of lower quality than the base material in terms of strength, plasticity, and gradation, but it is superior to the subgrade material in these properties. It may be compacted granular material or stabilized soil, thus allowing building up of sufficient thickness for the pavement structure at relatively low cost. On a weak subgrade, it also serves as a useful working platform for constructing the base course. Examples of grading requirements for subbase materials are given in Table 62.2. The
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COMPACTED SUBGRADE DEPTH-COHESIVE SOILS-INCHES
GROSS AIRCRAFT WEIGHT-DUAL TANDEM GEAR-1000 POUNDS 400 200 250 300 350 150 15 5 95% COHESIV E 100% N ONCOH ESIVE 20 25
10 90% CO
HESIVE
95%
30
NON
COH
ESIV
15
85%
ESIV
E
90%
45
NO
NC
25
35 40
COH
20
80%
E
COH
OH
ESI
VE
ESIV
50 55
E 85%
60
NO
NC
30
OH
ES
IVE
65 70
35 80
COMPACTED SUBGRADE DEPTH-NONCOHESIVE SOILS-INCHES
The Civil Engineering Handbook, Second Edition
75 110 140 170 200 230 GROSS AIRCRAFT WEIGHT-DUAL GEAR-1000 POUNDS
FIGURE 62.2 Subgrade compaction requirements for flexible airport pavements. (Source: Federal Aviation Administration, Airport Pavement Design and Evaluation, Advisory Circular AC 150/5320-6C, 1978, p. 41. With permission.)
subbase course may be omitted if the subgrade soil satisfies the requirements specified for subbase material. Prepared Subgrade Most natural soils forming the roadbed for pavement construction require some form of preparation or treatment. The top layer of a specified depth is usually compacted to achieve a desired density. The depth of compaction and the compacted density required depend on the type of soil and magnitudes of wheel loads and tire pressures. For highway construction, compaction to 100% modified AASHTO density covering a thickness of 12 in. (300 mm) below the formation level is commonly done. Compaction depth of up to 24 in. (600 mm) may be required for heavily trafficked pavements. For example, in the case of cohesive subgrade, the Asphalt Institute [1991] requires a minimum of 95% of AASHTO T180 (Method D) density for the top 12 in. (300 mm) and a minimum of 90% for all fill areas below the top 12 in. (300 mm). For cohesionless subgrade, the corresponding compaction requirements are 100 and 95%, respectively. Due to the higher wheel loads and tire pressures of aircraft, many stringent compaction requirements are found in airport pavement construction. Figure 62.2 shows an example of the compaction requirements recommended by the FAA [1978]. In some instances it may be economical to treat or stabilize poor subgrade materials and reduce the total required pavement thickness. Portland cement, lime, and bitumen have all been used successfully for this purpose. The choice of the method of stabilization depends on the soil properties, improvement expected, and cost of construction.
Rigid Pavement Rigid pavements constructed of portland cement concrete are mostly found in heavy-traffic highways and airport pavements. To allow for expansion, contraction, warping, or breaks in construction of the
Highway and Airport Pavement Design
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concrete slabs, joints are provided in concrete pavements. The joint spacing, which determines the length of individual slab panels, depends on the use of steel reinforcements in the slab. The jointed plain concrete pavement (JPCP), requiring no steel reinforcements and thus the least expensive to construct, is a popular form of construction. Depending on the thickness of the slab, typical joint spacings for plain concrete pavements are between 10 and 20 ft (3 and 6 m). For slabs with joint spacing greater than 6 m, steel reinforcements have to be provided for crack control, giving rise to the use of jointed reinforced concrete pavements (JRCP) and continuously reinforced concrete pavements (CRCP). Continuously reinforced concrete pavements usually contain higher than 0.6% steel reinforcement to eliminate the need to provide joints other than construction and expansion joints. The base course for rigid pavement, sometimes called subbase, is often provided to prevent pumping (ejection of foundation material through cracks or joints resulting from vertical movement of slabs under traffic). The base course material must provide good drainage and be resistant to the erosive action of water. When dowel bars are not provided in short jointed pavements, it is common practice to construct cement-treated base to assist in load transfer across the joints.
Considerations for Highway and Airport Pavements The two pavement types, flexible and rigid pavement, have been used for road and airport pavement construction. The choice of pavement type depends on the intended functional use of the pavement (such as operating speed and safety requirements), types of traffic loading, cost of construction, and maintenance consideration. The main differences in design considerations for highway and airport pavements arise from the characteristics of traffic using them. Over the typical design life span of 10 to 20 years for flexible pavements, or 20 to 40 years for rigid pavements, a highway pavement will be receiving highly channelized wheel load applications in the millions. Consideration of the effects of load repetitions — such as cumulative permanent deformation, crack propagation, and fatigue failure — becomes important. The total number of load applications in the entire design life of a highway pavement must therefore be known for pavement structural design. In contrast, the frequency of aircraft loading on airport pavement is much less. There are also the so-called wander effect of aircraft landing and taking off and the large variation in the wheel assembly configurations and layout of different aircraft. These make wheel loading on airport pavements less channelized than on highway pavements. Identification of the most critical aircraft is therefore necessary for structural design of airport pavements. Another important difference is in the magnitude of wheel loads. Airport pavements receive loads far exceeding those applied on the highway. An airport pavement may have to be designed to withstand equivalent single wheel loads of the order of 50 t (approximately 50 tons), whereas the maximum single wheel load allowed on the road pavement by most highway authorities is about 10 t (approximately 10 tons). Furthermore, the wheel tire pressure of an aircraft of about 1200 kPa (175 psi) is nearly twice the value of a normal truck tire. These differences greatly influence the material requirements for the pavements.
62.3 Traffic Loading Analysis for Highway Pavements Although it is convenient to describe the design life of a pavement in years, it is the total traffic loading during service that determines the actual design life of the pavement. It is thus more appropriate to associate the design life of a pavement with the total design traffic loading. For example, a pavement designed for 20 years with an assumed traffic growth of 4% will reach the end of its design life sooner than 20 years if the actual traffic growth is higher than 4%. The ultimate aim of traffic analysis for pavement design is to determine the magnitudes of wheel loads and the number of times each of these loads will be applied on the pavement during its design life. For highway pavements the computation of design traffic loading involves the following steps:
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1. 2. 3. 4. 5. 6.
The Civil Engineering Handbook, Second Edition
Estimation of expected initial year traffic volume Estimation of expected annual traffic growth rate Estimation of traffic stream composition Computation of traffic loads Estimation of directional split of design traffic loads Estimation of design lane traffic loads
Information concerning the first two steps can be obtained from traffic surveys and forecasts based on historical trends or prediction using transportation models. The analyses required for the remaining steps are explained in the discussions that follow.
Traffic Stream Composition The number of different types of vehicles — such as cars, buses, single-unit trucks, and multiple-unit trucks — expected to use the highways must be estimated. One may derive the vehicle-type distribution from results of classification counts made on similar highway type within the same region or from general data compiled by highway authorities, as illustrated in Table 62.4. However, as noted in the footnote of the table, individual situations may differ from the average values by 50% or more.
TABLE 62.4
Asphalt Institute Data for Truck Loading Computation Average Trucks Interstate Rural
Truck Class
Other Rural
All Rural
All Urban
All System
(a) Average Distribution on Different Classes of Highways (U.S.) Single-unit trucks 2 axle, 4 tire 2 axle, 6 tire 3 axle or more All single-unit Multiple-unit trucks 3 axle 4 axle 5 axle or more All multiple-unit All trucks
39 10 2 51
58 11 4 73
47 10 2 59
61 13 3 77
49 11 3 63
1 5 43 49 100
1 3 23 27 100
1 4 36 41 100
1 4 18 23 100
1 4 32 37 100
(b) Average Truck Factors (TF) for Different Classes of Highways and Vehicles (U.S.) Single-unit trucks 2 axle, 4 tire 2 axle, 6 tire 3 axle or more All single-unit Multiple-unit trucks 3 axle 4 axle 5 axle or more All multiple-unit All trucks
0.02 0.19 0.56 0.07
0.02 0.21 0.73 0.07
0.03 0.20 0.67 0.07
0.03 0.26 1.03 0.09
0.02 0.21 0.73 0.07
0.51 0.62 0.94 0.93 0.49
0.47 0.83 0.98 0.97 0.31
0.48 0.70 0.95 0.94 0.42
0.47 0.89 1.02 1.00 0.30
0.48 0.73 0.95 0.95 0.40
Note: Individual situations may differ from these average values by 50% or more. Source: Asphalt Institute, Asphalt Technology and Construction Practices. Educational Series ES-1, 1983b. pp. J5–J7. With permission.
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TABLE 62.5 Vehicle Classification by Axle Configuration Vehicle Class
Axle Configuration
Total No. of Axles
Number of Single Axles
Number of Tandem Axles
1
2
2
2
2
2
3
2
2
4
2
2
5
3
3
6
3
1
7
3
3
8
4
4
9
4
2
1
10
4
2
1
11
4
2
1
12
5
1
2
13
5
5
14
6
4
1
1
Source: Fwa, T.F. and Sinha, K.C., 1985. A Routine Maintenance and Pavement Performance Relationship Model for Highways, Report JHRP-85-11, Purdue University, West Lafayette, IN, 1985. With permission.
Traffic-Loading Computation Two aspects of traffic loading are of concern in the structural design of highway pavements, namely, the number of applications and the magnitude of each load type. A traffic count survey that classifies vehicles by axle configuration, as shown in Table 62.5, enables one to compute the number of repetitions by axle type (i.e., by single axle, tandem axle, and tridem axle). With this information, one must further subdivide each axle type by load magnitude to arrive at a traffic-loading table such as that illustrated in Table 62.6. The combined loading effects of different axle types on pavements cannot be easily analyzed. In the late 1950s, AASHO [Highway Research Board 1962] conducted the now well-known AASHO road test to provide, among other information, equivalency factors to convert one pass of any given single- or tandem-axle load to equivalent passes of an 18-kip (80 kN) single-axle load. The single-axle load of 18 kip (80 kN) was arbitrarily chosen in the AASHO road test as the standard axle with a damaging effect of unity. The equivalency factor, known as the equivalent single-axle load (ESAL) factor, was derived based on the relative damaging effects of various axle loads. Table 62.7 presents the ESAL factors of axle loads for different thicknesses of flexible pavements with a terminal serviceability index of 2.5. Table 62.8 presents the corresponding ESAL factors for rigid pavements. Another approach to computing the combined effect of mixed traffic is to adopt the hypothesis of cumulative damage. For a given form of pavement damage, the allowable number of repetitions by each vehicle type or load group is established separately. A damage ratio for vehicle type or load group i is defined as Di = ( ni § Ni )
(62.1)
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The Civil Engineering Handbook, Second Edition
TABLE 62.6
Examples of Axle-Load Data Presentation
Single Axle
Tandem Axle
Axle Load (kips)
No. Axles/Day
Axle Load (kips)
No. Axles/Day
Less than 3 3–5 5–7 7–9 9–11 11–13 13–15 15–17 17–19 19–21 21–23
1438 3391 3432 6649 9821 2083 946 886 472 299 98
9–11 11–13 13–15 15–17 17–19 19–21 21–23 23–25 25–27 27–29 29–31 31–33 33–35 35–37 37–39 39–41
2093 1867 1298 1465 1734 1870 2674 2879 2359 2104 1994 1779 862 659 395 46
where ni is the design repetitions and Ni the allowable repetitions. The total level of damage caused by the mixed traffic is computed as the sum of damage ratios of all vehicle types or load groups. Example 62.1 This example involves computation of the ESAL contribution of a passenger car, a bus, and a combination truck. The axle loads of the three fully laden vehicles are given as follows: Car. Front single axle = 2 kips; rear single axle = 2 kips. Bus. Front single axle = 10 kips; rear single axle = 8 kips. Truck. Front single axle = 12 kips; middle single axle = 18 kips; rear tandem axle = 32 kips. Assuming a terminal serviceability index of 2.5, the ESAL contributions of the three vehicles can be computed for a flexible pavement with structural number SN = 5.0 [see Eq. (62.17) for definition of SN] and a rigid pavement of slab thickness equal to 10 in. For the ESAL on flexible pavement, Table 62.7 is used to obtain the ESAL factor for each axle. The ESAL contribution of the passenger car is (0.0002 + 0.0002) = 0.0004. The ESAL contribution of the bus is (0.088 + 0.034) = 0.122. The contribution of the truck is (0.189 + 1.00 + 0.857) = 2.046. Table 62.8 is used for the ESAL computation in the case of rigid pavement. The ESAL contributions are (0.0002 + 0.0002) = 0.0004 for the car, (0.081 + 0.032) = 0.113 for the bus, and (0.175 + 1.00 + 1.50) = 2.675 for the truck. The ratios of ESAL contributions are (car):(bus):(truck) = 5012:305:1 for flexible pavement and 6688:283:1 for rigid pavement. It can be seen from this example that the damaging effects of a truck and a bus are, respectively, more than 5000 and 280 times that of a passenger car. This explains why passenger car volumes are often ignored in traffic-loading computation for pavement design. Example 62.2 This example involves ESAL computation based on axle load data. Calculate the total daily ESAL of the traffic-loading data of Table 62.6 for (a) a flexible pavement with structural number SN = 5.0 [see Eq. (62.17) for definition of SN] and (b) a rigid pavement with slab thickness of 10 in. The design terminal serviceability index for both pavements is 2.5. The data in Table 62.6 are repeated in columns (1) and (2) of the following table. The ESAL factors in column (3) are obtained from Table 62.7 (second part) for SN = 5.0, and those in column (5) are obtained from Table 62.8 (second part) for slab thickness of 10 in. The ESAL contribution by each axle
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Highway and Airport Pavement Design
group is computed by multiplying its ESAL factor by the number of axles per day. The total ESAL of the traffic loading is 12,642 for the flexible pavement and 19,309 for the rigid pavement. Axle Load (kips) (1)*
No. Axles per Day (2)
S2 S4 S6 S8 S10 S12 S14 S16 S18 S20 S22 T10 T12 T14 T16 T18 T20 T22 T24 T26 T28 T30 T32 T34 T36 T38 T40
1438 3391 3432 6649 9821 2083 946 886 472 299 98 2093 1867 1298 1465 1734 1870 2674 2879 2359 2104 1994 1779 862 659 395 46
*
Flexible Pavement ESAL Factor (3)
Rigid Pavement
ESAL (2) ¥ (3)
ESAL Factor (5)
0.0002 0.2876 0.002 6.782 0.01 34.32 0.034 226.066 0.088 864.248 0.189 393.687 0.36 340.56 0.623 551.978 1.00 472.00 1.51 451.49 2.18 213.64 0.007 14.651 0.014 26.138 0.027 35.046 0.047 68.855 0.077 133.518 0.121 226.27 0.18 481.32 0.26 748.54 0.364 858.676 0.495 1041.48 0.658 1312.052 0.857 1524.603 1.09 939.58 1.38 909.42 1.7 671.5 2.08 95.68 Total = 12,642.38
ESAL (2) ¥ (5)
0.0002 0.2876 0.002 6.782 0.01 34.32 0.032 212.768 0.081 795.501 0.175 364.525 0.338 319.748 0.601 532.486 1.00 472.00 1.58 472.42 2.38 233.24 0.012 25.116 0.025 46.675 0.047 61.006 0.081 118.665 0.132 228.888 0.204 381.48 0.305 815.57 0.441 1269.639 0.62 1462.58 0.85 1788.4 1.14 2273.16 1.5 2668.5 1.95 1680.9 2.48 1634.32 3.12 1232.4 3.87 178.02 Total = 19,309.39
In column (1), the prefix S stands for single axle and T stands for tandem axle.
TABLE 62.7 Axle Load (kips)
AASHTO Load Equivalency Factors for Flexible Pavements Pavement Structural Number (SN) 1
2
3
4
5
6
.0002 .002 .010 .034 .088 .189 .360 .623 1.00 1.51 2.18 3.03 4.09 5.39 7.0
.0002 .002 .009 .031 .080 .176 .342 .606 1.00 1.55 2.30 3.27 4.48 5.98 7.8
(a) Single Axles and pt of 2.5 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
.0004 .003 .011 .032 .078 .168 .328 .591 1.00 1.61 2.48 3.69 5.33 7.49 10.3
.0004 .004 .017 .047 .102 .198 .358 .613 1.00 1.57 2.38 3.49 4.99 6.98 9.5
.0003 .004 .017 .051 .118 .229 .399 .646 1.00 1.49 2.17 3.09 4.31 5.90 7.9
.0002 .003 .013 .041 .102 .213 .388 .645 1.00 1.47 2.09 2.89 3.91 5.21 6.8
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The Civil Engineering Handbook, Second Edition
TABLE 62.7 (continued) AASHTO Load Equivalency Factors for Flexible Pavements Axle Load (kips) 32 34 36 38 40 42 44 46 48 50
Pavement Structural Number (SN) 1
2
3
4
5
6
13.9 18.4 24.0 30.9 39.3 49.3 61.3 75.5 92.2 112.
12.8 16.9 22.0 28.3 35.9 45.0 55.9 68.8 83.9 102.
10.5 13.7 17.7 22.6 28.5 35.6 44.0 54.0 65.7 79.
8.8 11.3 14.4 18.1 22.5 27.8 34.0 41.4 50.1 60.
8.9 11.2 13.9 17.2 21.1 25.6 31.0 37.2 44.5 53.
10.0 12.5 15.5 19.0 23.0 27.7 33.1 39.3 46.5 55.
.0000 .0003 .001 .003 .007 .014 .027 .047 .077 .121 .180 .260 .364 .495 .658 .857 1.09 1.38 1.70 2.08 2.51 3.00 3.55 4.17 4.86 5.63 6.47 7.4 8.4 9.6 10.8 12.2 13.7 15.4 17.2 19.2 21.3 23.7 26.2 29.0 32.0 35.3
.0000 .0002 .001 .003 .006 .013 .024 .043 .070 .110 .166 .242 .342 .470 .633 .834 1.08 1.38 1.73 2.14 2.61 3.16 3.79 4.49 5.28 6.17 7.15 8.2 9.4 10.7 12.1 13.7 15.4 17.2 19.2 21.3 23.6 26.1 28.8 31.7 34.8 38.1
(b) Tandem Axles and pt of 2.5 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84
.0001 .0005 .002 .004 .008 .015 .026 .044 .070 .107 .160 .231 .327 .451 .611 .813 1.06 1.38 1.75 2.21 2.76 3.41 4.18 5.08 6.12 7.33 8.72 10.3 12.1 14.2 16.5 19.1 22.1 25.3 29.0 33.0 37.5 42.5 48.0 54.0 60.6 67.8
.0001 .0005 .002 .006 .013 .024 .041 .065 .097 .141 .198 .273 .370 .493 .648 .843 1.08 1.38 1.73 2.16 2.67 3.27 3.98 4.80 5.76 6.87 8.14 9.6 11.3 13.1 15.3 17.6 20.3 23.3 26.6 30.3 34.4 38.9 43.9 49.4 55.4 61.9
.0001 .0004 .002 .005 .011 .023 .042 .070 .109 .162 .229 .315 .420 .548 .703 .889 1.11 1.38 1.69 2.06 2.49 2.99 3.58 4.25 5.03 5.93 6.95 8.1 9.4 10.9 12.6 14.5 16.6 18.9 21.5 24.4 27.6 31.1 35.0 39.2 43.9 49.0
.0000 .0003 .001 .004 .009 .018 .033 .057 .092 .141 .207 .292 .401 .534 .695 .887 1.11 1.38 1.68 2.03 2.43 2.88 3.40 3.98 4.64 5.38 6.22 7.2 8.2 9.4 10.7 12.2 13.8 15.6 17.6 19.8 22.2 24.8 27.8 30.9 34.4 38.2
62-13
Highway and Airport Pavement Design
TABLE 62.7 (continued) AASHTO Load Equivalency Factors for Flexible Pavements Axle Load (kips) 86 88 90
Pavement Structural Number (SN) 1
2
3
4
5
6
75.7 84.3 93.7
69.1 76.9 85.4
54.5 60.6 67.1
42.3 46.8 51.7
38.8 42.6 46.8
41.7 45.6 49.7
.0000 .0001 .0003 .001 .002 .003 .006 .011 .017 .027 .040 .057 .080 .109 .145 .191 .246 .313 .393 .487 .597 .723 .868 1.033 1.22 1.43 1.66 1.91 2.20 2.51 2.85 3.22 3.62 4.05 4.52 5.03 5.57 6.15 6.78 7.45 8.2 8.9 9.8 10.6 11.6
.0000 .0001 .0003 .001 .002 .003 .006 .010 .016 .024 .036 .051 .072 .099 .133 .175 .228 .292 .368 .459 .567 .692 .838 1.005 1.20 1.41 1.66 1.93 2.24 2.58 2.95 3.36 3.81 4.30 4.84 5.41 6.04 6.71 7.43 8.21 9.0 9.9 10.9 11.9 12.9
(c) Triple Axles and pt of 2.5 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90
.0000 .0002 .0006 .001 .003 .005 .008 .012 .018 .027 .038 .053 .072 .098 .129 .169 .219 .279 .352 .439 .543 .666 .811 .979 1.17 1.40 1.66 1.95 2.29 2.67 3.09 3.57 4.11 4.71 5.38 6.12 6.93 7.84 8.83 9.92 11.1 12.4 13.8 15.4 17.1
.0000 .0002 .0007 .002 .004 .007 .012 .019 .029 .042 .058 .078 .103 .133 .169 .213 .266 .329 .403 .491 .594 .714 .854 1.015 1.20 1.41 1.66 1.93 2.25 2.60 3.00 3.44 3.94 4.49 5.11 5.79 6.54 7.37 8.28 9.28 10.4 11.6 12.9 14.3 15.8
.0000 .0002 .0005 .001 .003 .006 .010 .018 .028 .042 .060 .084 .114 .151 .195 .247 .308 .379 .461 .554 .661 .781 .918 1.072 1.24 1.44 1.66 1.90 2.17 2.48 2.82 3.19 3.61 4.06 4.57 5.13 5.74 6.41 7.14 7.95 8.8 9.8 10.8 11.9 13.2
.0000 .0001 .0004 .001 .002 .004 .008 .013 .021 .032 .048 .068 .095 .128 .170 .220 .281 .352 .436 .533 .644 .769 .911 1.069 1.25 1.44 1.66 1.90 2.16 2.44 2.76 3.10 3.47 3.88 4.32 4.80 5.32 5.88 6.49 7.15 7.9 8.6 9.5 10.4 11.3
Source: AASHTO Guides for Design of Pavement Structures, American Association of State Highway and Transportation Officials, Washington, D.C., 1993. With permission.
62-14
TABLE 62.8 Axle Load (kips)
The Civil Engineering Handbook, Second Edition
AASHTO Load Equivalency Factors for Rigid Pavements Slab Thickness, D (inches) 6
7
8
9
10
11
12
13
14
.0002 .002 .010 .032 .080 .174 .337 .599 1.00 1.58 2.40 3.50 4.95 6.81 9.14 12.0 15.4 19.5 24.3 29.9 36.3 43.8 52.3 62.1 73.3
.0002 .002 .010 .032 .080 .174 .336 .599 1.00 1.59 2.41 3.53 5.01 6.92 9.35 12.3 16.0 20.4 25.6 31.6 38.7 46.7 55.9 66.3 78.1
.0002 .002 .010 .032 .080 .173 .336 .599 1.00 1.59 2.41 3.54 5.04 6.98 9.46 12.6 16.4 21.0 26.4 32.9 40.4 49.1 59.0 70.3 83.0
.0002 .002 .010 .032 .080 .173 .336 .598 1.00 1.59 2.41 3.55 5.05 7.01 9.52 12.7 16.5 21.3 27.0 33.7 41.6 50.8 61.4 73.4 87.1
.0001 .0005 .002 .005 .012 .025 .047 .081 .131 .203 .304 .440 .619 .850 1.14 1.51 1.96 2.51 3.16 3.94 4.86 5.92 7.14 8.55 10.14 11.9 13.9
.0001 .0005 .002 .005 .012 .025 .047 .080 .131 .203 .303 .439 .618 .849 1.14 1.51 1.97 2.52 3.18 3.98 4.91 6.01 7.28 8.75 10.42 12.3 14.5
.0001 .0005 .002 .005 .012 .025 .047 .080 .131 .203 .303 .439 .618 .849 1.14 1.51 1.97 2.52 3.20 4.00 4.95 6.06 7.36 8.86 10.58 12.5 14.8
.0001 .0005 .002 .005 .012 .025 .047 .080 .131 .203 .303 .439 .618 .849 1.14 1.51 1.97 2.53 3.20 4.01 4.96 6.09 7.40 8.92 10.66 12.7 14.9
(a) Single Axles and pt of 2.5 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
.0002 .003 .012 .039 .097 .203 .376 .634 1.00 1.51 2.21 3.16 4.41 6.05 8.16 10.8 14.1 18.2 23.1 29.1 36.2 44.6 54.5 66.1 79.4
.0002 .002 .011 .035 .089 .189 .360 .623 1.00 1.52 2.20 3.10 4.26 5.76 7.67 10.1 13.0 16.7 21.1 26.5 32.9 40.4 49.3 59.7 71.7
.0002 .002 .010 .033 .084 .181 .347 .610 1.00 1.55 2.28 3.22 4.42 5.92 7.79 10.1 12.9 16.4 20.6 25.7 31.7 38.8 47.1 56.9 68.2
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54
.0001 .0006 .002 .007 .015 .031 .057 .097 .155 .234 .340 .475 .644 .855 1.11 1.43 1.82 2.29 2.85 3.52 4.32 5.26 6.36 7.64 9.11 10.8 12.8
.0001 .0006 .002 .006 .014 .028 .052 .089 .143 .220 .325 .462 .637 .854 1.12 1.44 1.82 2.27 2.80 3.42 4.16 5.01 6.01 7.16 8.50 10.0 11.8
.0001 .0005 .002 .006 .013 .026 .049 .084 .136 .211 .313 .450 .627 .852 1.13 1.47 1.87 2.35 2.91 3.55 4.30 5.16 6.14 7.27 8.55 10.0 11.7
.0002 .002 .010 .032 .082 .176 .341 .604 1.00 1.57 2.34 3.36 4.67 6.29 8.28 10.7 13.6 17.1 21.3 26.3 32.2 39.2 47.3 56.8 67.8
.0002 .002 .010 .032 .081 .175 .338 .601 1.00 1.58 2.38 3.45 4.85 6.61 8.79 11.4 14.6 18.3 22.7 27.9 34.0 41.0 49.2 58.7 69.6
(b) Tandem Axles and pt of 2.5 .0001 .0005 .002 .005 .013 .026 .048 .082 .133 .206 .308 .444 .622 .850 1.14 1.49 1.92 2.43 3.03 3.74 4.55 5.48 6.53 7.73 9.07 10.6 12.3
.0001 .0005 .002 .005 .012 .025 .047 .081 .132 .204 .305 .441 .620 .850 1.14 1.50 1.95 2.48 3.12 3.87 4.74 5.75 6.90 8.21 9.68 11.3 13.2
62-15
Highway and Airport Pavement Design
TABLE 62.8 (continued) AASHTO Load Equivalency Factors for Rigid Pavements Axle Load (kips) 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90
Slab Thickness, D (inches) 6 15.0 17.5 20.3 23.5 27.0 31.0 35.4 40.3 45.7 51.7 58.3 65.5 73.4 82.0 91.4 102. 113. 125.
7
8
9
13.8 16.0 18.5 21.4 24.6 28.1 32.1 36.5 41.4 46.7 52.6 59.1 66.2 73.9 82.4 92. 102. 112.
13.6 15.7 18.1 20.8 23.8 27.1 30.9 35.0 39.6 44.6 50.2 56.3 62.9 70.2 78.1 87. 96. 106.
.0001 .0003 .001 .002 .005 .010 .018 .030 .048 .073 .107 .151 .209 .281 .371 .480 .609 .762 .941 1.15 1.38 1.65 1.96 2.31 2.71 3.15 3.66 4.23 4.87 5.59 6.39 7.29 8.28 9.4 10.6 12.0
.0001 .0003 .001 .002 .005 .010 .017 .029 .045 .069 .101 .144 .200 .271 .359 .468 .601 .759 .946 1.16 1.41 1.70 2.03 2.40 2.81 3.27 3.79 4.37 5.00 5.71 6.50 7.37 8.33 9.4 10.6 11.8
14.2 16.3 18.7 21.4 24.4 27.6 31.3 35.3 39.8 44.7 50.1 56.1 62.5 69.6 77.3 86. 95. 105.
10
11
12
13
14
15.2 17.5 20.0 22.8 25.8 29.2 32.9 37.0 41.5 46.4 51.8 57.7 64.2 71.2 78.9 87. 96. 106.
16.2 18.6 21.4 24.4 27.7 31.3 35.2 39.5 44.2 49.3 54.9 60.9 67.5 74.7 82.4 91. 100. 110.
16.8 19.5 22.5 25.7 29.3 33.2 37.5 42.1 47.2 52.7 58.6 65.0 71.9 79.4 87.4 96. 105. 115.
17.3 20.1 23.2 26.7 30.5 34.7 39.3 44.3 49.8 55.7 62.1 69.0 76.4 84.4 93.0 102. 112. 123.
17.5 20.4 23.6 27.3 31.3 35.7 40.5 45.9 51.7 58.0 64.8 72.3 80.2 88.8 98.1 108. 119. 130.
.0001 .0003 .001 .002 .005 .009 .016 .027 .043 .066 .097 .139 .193 .262 .350 .459 .593 .755 .951 1.18 1.46 1.78 2.15 2.58 3.07 3.62 4.26 4.97 5.76 6.64 7.62 8.70 9.88 11.2 12.6 14.1
.0001 .0003 .001 .002 .005 .009 .016 .027 .043 .066 .097 .138 .192 .262 .349 .458 .592 .755 .951 1.18 1.46 1.78 2.16 2.59 3.09 3.66 4.30 5.03 5.85 6.77 7.79 8.92 10.17 11.5 13.0 14.7
.0001 .0003 .001 .002 .005 .009 .016 .027 .043 .066 .097 .138 .192 .262 .349 .458 .592 .755 .951 1.18 1.46 1.78 2.16 2.60 3.10 3.68 4.33 5.07 5.90 6.84 7.88 9.04 10.33 11.7 13.3 15.0
.0001 .0003 .001 .002 .005 .009 .016 .027 .043 .066 .097 .138 .192 .262 .349 .458 .592 .755 .951 1.18 1.46 1.79 2.16 2.60 3.11 6.68 4.34 5.09 5.93 6.87 7.93 9.11 10.42 11.9 13.5 15.2
(c) Triple Axles and pt of 2.5 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72
.0001 .0003 .001 .003 .006 .011 .020 .033 .053 .080 .116 .163 .222 .295 .384 .490 .616 .765 .939 1.14 1.38 1.65 1.97 2.34 2.76 3.24 3.79 4.41 5.12 5.91 6.80 7.79 8.90 10.1 11.5 13.0
.0001 .0003 .001 .002 .005 .009 .017 .028 .044 .067 .099 .141 .195 .265 .354 .463 .596 .757 .948 1.17 1.44 1.74 2.09 2.49 2.94 3.44 4.00 4.63 5.32 6.08 6.91 7.82 8.83 9.9 11.1 12.4
.0001 .0003 .001 .002 .005 .009 .016 .027 .044 .066 .098 .139 .194 .263 .351 .460 .594 .756 .950 1.18 1.45 1.77 2.13 2.55 3.02 3.56 4.16 4.84 5.59 6.42 7.33 8.33 9.42 10.6 11.9 13.3
62-16
The Civil Engineering Handbook, Second Edition
TABLE 62.8 (continued) AASHTO Load Equivalency Factors for Rigid Pavements Axle Load (kips) 74 76 78 80 82 84 86 88 90
Slab Thickness, D (inches) 6
7
8
9
14.6 16.5 18.5 20.6 23.0 25.6 28.4 31.5 34.8
13.5 15.1 16.9 18.8 21.0 23.3 25.8 28.6 31.5
13.2 14.8 16.5 18.3 20.3 22.5 24.9 27.5 30.3
13.8 15.4 17.1 18.9 20.9 23.1 25.4 27.9 30.7
10
11
14.8 16.5 18.2 20.2 22.2 24.5 26.9 29.4 32.5
15.8 17.6 19.5 21.6 23.8 26.2 28.8 31.5 34.4
12 16.5 18.4 20.5 22.7 25.2 27.8 30.5 33.5 36.7
13 16.9 18.9 21.1 23.5 26.1 28.9 31.9 35.1 38.5
14 17.1 19.2 21.5 24.0 26.7 29.6 32.8 36.1 39.8
Source: AASHTO Guides for Design of Pavement Structures, American Association of State Highway and Transportation Officials, Washington, D.C., 1993. With permission.
Example 62.3 This example entails ESAL computation based on Asphalt Institute truck distribution and truck factors. Consider a two-lane rural highway with a design lane daily directional traffic of 2000 vehicles per day during the first year. The traffic growth factor is 4.5% and there are 16% trucks in the traffic. The total number of trucks in the 20-year design traffic is computed by the following geometric sum equation: ( 1 + 0.01 ¥ 4.5 ) – 1 ( 2000 ¥ 365 ¥ 16% ) ◊ -------------------------------------------------- = 3, 664 ,180 0.01 ¥ 4.5 20
The following table summarizes the procedure for ESAL computation. The numbers of vehicles in column (2) are calculated based on the distribution of “other rural” in Table 62.4(a) and the truck factors in column (3) are for “other rural” given in Table 62.4(b). Vehicle Type (1)
Number of Vehicles (2)
Truck Factor (3)
ESAL Contribution (4)
Single-Unit Trucks 2-axle, 4-tire 2-axle, 6-tire 3-axle or more All singles
2,125,220 403,060 146,570 2,674,850
0.02 0.21 0.73
45,200 84,640 107,000 236,840
Tractor Semitrailers and Combinations 3-axle 4-axle 5-axle or more All multiple units
36,640 109,930 842,760 989,330
0.48 0.70 0.95
17,590 76,950 800,620 895,160
Total design ESAL = 1,132,000
Directional Split It is common practice to report traffic volume of a highway to include flows for all lanes in both directions. To determine the design traffic loading on the design lane, one must split the traffic by direction and distribute the directional traffic by lanes. An even split assigning 50% of the traffic to each direction appears to be the norm. In circumstances where an uneven split occurs, pavements are designed based on the heavier directional traffic loading.
62-17
Highway and Airport Pavement Design
(b) Recommendation by Asphalt Institute [1991]
ADT (One Direction), Thousands
100 60 2 Lanes in One Direction
Number of Lanes per Direction 1 2 3 or more
20 10 6 4
3 Lanes in One Direction
Number of Lanes per Direction 0.6
0.7
100% 90% (70-96%) 80% (50-96%)
(c) Recommendation by AASHTO [1993]
2 0 0.5
% Trucks in Design Lane
0.8
0.9
1.0
1 2 3 4
Proportion of Trucks in Right Lane
% ESAL in Design Lane 100% 80-100% 60-80% 50-75%
Note: ESAL stands for equivalent 80 kN single axle load
FIGURE 62.3 Percentage of truck traffic in design lane.
Design Lane Traffic Loading The design lane for pavement structural design is usually the slow lane (lane next to the shoulder in most cases), in which a large proportion of the directional heavy-vehicle traffic is expected to travel. Some highway agencies assign 100% of the estimated directional heavy-vehicle traffic to the design lane for the purpose of structural design. This leads to overestimation of traffic loading on roads with more than one lane in each direction. Studies have shown that — depending upon road geometry, traffic volume, and composition — as much as 50% of the directional heavy vehicles may not travel on the design lane [Fwa and Li, 1994]. Figure 62.3 shows the lane-use distributions recommended by a number of organizations. It is noted that while most agencies apply lane-use factors to traffic volume, the factors in AASHTO recommendations are for lane distributions of ESAL. The latter tends to provide a better estimate of traffic loading in cases involving a higher concentration of heavily loaded vehicles in the slow lane.
Formula for Computing Total Design Loading Depending on the information available, the computations of the design load for pavement structural design may differ slightly. Assuming that the initial-year total ESAL is known and a constant growth of ESAL at a rate of r% per annum is predicted, the design lane loading for an analysis period of n years can be computed by the following equation: ( 1 + 0.01r ) – 1 ( ESAL ) T = ( ESAL ) 0 ◊ ------------------------------------- ◊ f D ◊ f L 0.01r n
where (ESAL)T = total design lane ESAL for n years (ESAL)0 = initial-year design lane ESAL r = annual growth rate of ESAL in percent fD = directional split factor fL = lane-use distribution factor
(62.2)
62-18
The Civil Engineering Handbook, Second Edition
For design methods that rely on damage ratio computation [see Eq. (62.1)], instead of computing cumulative ESAL, the total number of repetitions of each vehicle type or axle type is calculated. Example 62.4 The daily ESAL computed in Example 62.2 is based on the initial traffic estimate for both directions of travel in an expressway with three lanes in each direction. The annual growth of traffic is estimated at 3%. The directional split is assumed to be 45 to 55%. The expressway is to be constructed of flexible pavement. Calculate the design lane ESAL for a service life of 15 years. Adopting the AASHTO lane distribution factor shown in Fig. 62.3(b), we have fL = 0.7. Given fD = 0.55, n = 15, and i = 3, and from Example 62.2 (ESAL)0 = (12,642 ¥ 365), the total design lane ESAL is ( 1 + 0.01 ¥ 3 ) – 1 ( ESAL ) T = ( 12, 642 ¥ 365 ) ◊ ---------------------------------------------- ◊ 0.7 ◊ 0.55 0.01 ¥ 3 15
= 33.04 ¥ 10
6
62.4 Traffic Loading Analysis for Airport Pavements The procedure of traffic loading analysis for airport pavements differs slightly from that for highway pavements due to differences in traffic operations and functional uses of the pavements. The basic steps are: 1. 2. 3. 4. 5.
Estimation of expected initial year traffic volume Estimation of expected annual traffic growth rate Estimation of traffic stream composition Computation of traffic loading Estimation of design traffic loading for different functional areas
Information concerning the first two steps is usually obtained from the planning forecast of the airport authority concerned.
Traffic Stream Composition The weight of an aircraft is transmitted to the pavement through its nose gear and main landing gears. Figure 62.4 shows the wheel configurations commonly found on the main legs of landing gear of civil aircraft. Since the gross weight and exact arrangement of wheels differ among different aircraft, there is a need to identify the types of aircraft, landing gear details, and their respective frequencies of arrival for the purpose of pavement design.
Computation of Traffic Loading For pavement design purposes, the maximum takeoff weights of the aircraft are usually considered. It is also common to assume that 95% of the gross weight is carried by the main landing gears and 5% by the nose gear. In the consideration of mixed traffic loading, both the equivalent load concept and Miner’s hypothesis have been used. For example, the FAA method [Federal Aviation Administration, 1978] converts the annual departure of all aircraft into the equivalent departures of a selected design aircraft using the factors in Table 62.9. In establishing the thickness design curves for flexible airport pavements, the concept of equivalent single-wheel load (ESWL) is adopted by the FAA. The concept of ESWL is widely used in airport pavement design to assess the effect of multiple-wheel landing gears. The value of ESWL of a given landing gear varies with the control response selected for ESWL computation,
62-19
Highway and Airport Pavement Design
Single Wheel Landing Gear (Example : DC-3)
Double Dual Tandem Landing Gear (Example : B747-100) Nose Wheel
Nose Wheel
Landing Gear
Landing Gear
Dual Tandem Landing Gear (Example : B767-200)
Dual Wheel Landing Gear (Example : DC-6)
Nose Gear
Nose Gear
Landing Gear
Landing Gear
FIGURE 62.4 Typical wheel configurations of a main leg of aircraft landing gear.
TABLE 62.9 Conversion Factors for Computing Annual Departures Aircraft Type Single-wheel Single-wheel Dual-wheel Double dual-tandem Dual-tandem Dual-tandem Dual-wheel Double dual-tandem
Design Aircraft
Conversion Factor F
Dual-wheel Dual-tandem Dual-tandem Dual-tandem Single-wheel Dual-wheel Single-wheel Dual-wheel
0.8 0.5 0.6 1.0 2.0 1.7 1.3 1.7
Note: Multiply the annual departures of given aircraft type by the conversion factor to obtain annual departures in design aircraft landing gear. 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.
thickness of pavement, and the relative stiffness of pavement layers. For airport pavement design, ESWL computations based on equal deflection (at surface or at pavement–subgrade interface) or equal stress (at bottom face of bound layer) are commonly used.
62-20
The Civil Engineering Handbook, Second Edition
Example 62.5 This example concerns the representation of annual departures of designed aircraft. An airport pavement is to be designed for the following estimated traffic: In this example, the 727-200 requires the greatest pavement thickness and is therefore the design aircraft. The conversion factors are obtained from Table 62.9. The entries in the last column are the products of the conversion factors and the estimated annual departures.
Aircraft 727-100 727-200 707-320B DC-9-30 747-100
Landing Gear Type
Est. Annual Departures
Max. Wt. (kips)
Conversion Factor
Converted Annual Departures
Dual Dual Dual tandem Dual Dual DT
4500 9900 3200 5500 60
160 190.5 327 108 700
1.0 1.0 1.7 1.0 1.7
4500 9900 5440 5500 102
Equal Stress ESWL An elaborate procedure for computing the ESWL would call for both a proper analytical solution for the required stress produced by the wheel assembly of interest and a trial-and-error process to identify the magnitude of the single wheel that will produce identical stress. As this procedure is time consuming, simplified methods have been employed in practice. Figure 62.5(a) presents a simplified procedure for estimating the equal subgrade stress ESWL of a set of dual wheels for flexible pavement design. With the assumed 45˚ spread of applied pressure, the ESWL is equal to one wheel load P if the pavement thickness is less than or equal to d/2, where d is the smallest edge-to-edge distance between the tire imprints of the dual wheels. The method further assumes that ESWL = 2P for any pavement equal to or thicker than 2S, where S is the center-to-center spacing of the dual wheels. For pavement thicknesses between d/2 and 2S, ESWL is determined, as shown in Fig. 62.5(a), by assuming a linear log–log relationship between ESWL and pavement thickness. Note that d is equal to (S – 2a), where a is the radius of tire imprint given by a =
P -----pp
(62.3)
where p is the tire pressure. This simplified procedure provides an approximate ESWL estimation for flexible pavements. In the case of rigid pavements, computation of stresses for equal stress ESWL should be based on rigid slab analysis such as the well-known Westergaard formulas, which give the maximum bending stress smax and the maximum deflection dmax as shown below. smax and dmax under interior loading [Westergaard, 1926] are given as
where
3P ( 1 + m ) Ê bˆ 2 3P ( 1 + m ) Ê 2Lˆ - ln ------ + 0.5 – g + ----------------------- --s max = ----------------------2 2 Ë L¯ Ë b¯ 2ph 64h
(62.4)
2 ¸ P Ï a aˆ d max = -----------2 Ì 1 + ------------2 ln Ê ----- + g – 1.25 ˝ Ë ¯ 2L 8kL Ó 2pL ˛
(62.5)
b = (1.6a2 + h2)0.5 – 0.675h, a < 1.724h = a, a > 1.724h P = total applied load m = slab Poisson’s ratio
62-21
Highway and Airport Pavement Design
2P
Log (Load)
P
P
d s (ESWL) P z = depth of pavement structure d/2
(a)
1.5
z
2S
Log (Depth below pavement surface)
0.0 Offset radii 0.5
1.0
Radii =
1.0
0.9
Single-tire contact area p
0.8 0.7 0.6
1.5
0.5 2.0
0.4
2.5 Deflection factor
0.3 3.0 3.5 0.2
4.0
0.18 0.16
5.0
0.14
6.0
0.12
7.0
0.10 0.09
8.0 9.0 10.0
0.08 0.07
12.0
0.06
14.0
0.05
16.0 17.5
0.04
0.03
(b)
0
1
2
3
4
5
6 7 Depth (radii)
8
9
10
11
12
FIGURE 62.5 Computation of ESWL. (a) Equal subgrade stress ESWL of dual wheels for flexible pavement design. (b) One-layer deflection factor for equal-deflection ESWL computation. (Source: Yoder, E.J. and Witczak, M.W., Principles of Pavement Design, 2nd ed., John Wiley & Sons, New York, 1975, p. 138. With permission.)
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The Civil Engineering Handbook, Second Edition
h = slab thickness L = radius of relative stiffness a = radius of loaded area k = modulus of subgrade reaction g = Euler’s constant = 0.577216 smax and dmax under edge loading [Westergaard, 1926, 1933, 1948] are given as 3 3 ( 1 + m )P Ï 11 ¸ Ê aˆ Eh s max = --------------------------2 Ì ln --------------------4 + 1.18 Ë ---¯ ( 1 + 2 m ) + 2.34 – ----- m ˝ L 6 ˛ p ( 3 + m )h Ó 100k ( a )
( 2 + 1.2 m ) d max = P -----------------------3 Eh k
0.5
Ï Ê aˆ ¸ Ì 1 – ( 0.76 + 0.4 m ) Ë ---¯ ˝ L ˛ Ó
(62.6)
(62.7)
where E = slab elastic modulus and all other variables are as defined in Eqs. (62.1) and (62.2). smax and d max under corner loading [Westergaard 1926] are given as 3P 1.4142a 0.6 s max = -----2- ÊË 1 – ÊË -------------------ˆ¯ ˆ¯ L h
(62.8)
P 1.4142a d max = --------2 ÊË 1.1 – 0.88 ÊË -------------------ˆ¯ ˆ¯ L kL
(62.9)
Example 62.6 This example addresses equal subgrade stress ESWL. The total load on a set of dual wheels is 45,000 lb. The tire pressure of the wheels is 185 psi. The center-to-center spacing of the wheels is 34 in. Calculate the equal stress ESWL if the thickness of pavement structure is (a) h = 30 in. and (b) h = 70 in. Load per wheel = 22,500 lb., radius of tire imprint a = ( 22, 500 /185 p ) = 6.22 in., S = 34 in., and d = (S – 2a) = 21.56. By means of a log–log plot as shown in Fig. 62.5(a), ESWL is determined to be 33,070 lb. for h = 30 in. For h = 70 in., since h > 2S, ESWL = 2(22,500) = 45,000 in.
Equal Deflection ESWL Equal deflection ESWL can be derived by assuming either constant tire pressure or constant area of tire imprint. A simplified method for computing ESWL on flexible pavement, based on the Boussinesq onelayer theory [Boussinesq, 1885], is presented in this section. It computes the ESWL of an assembly of n wheels by equating the surface deflection under the ESWL to the maximum surface deflection caused by the wheel assembly, that is, 0.5 ( ESWL ) 0.5 P --------------------------K = -------- ( K 1 + K 2 + L + K n ) max pE pE
(62.10)
where
P = gross load on each tire of the wheel assembly E = stiffness modulus of the soil K, K1, K2, Kn = Boussinesq deflection factor given by Fig. 62.5(b)
With the assumption of constant tire pressure, Eq. (62.2) can be solved for ESWL by the following iterative procedure: (1) compute (K1 + K2 + L + Kn)max at the point of maximum surface deflection; (2) assume a, the radius of tire imprint for ESWL; (3) determine K from Fig. 62.5(b) with zero horizontal
62-23
Highway and Airport Pavement Design
offset; (4) compute ESWL from Eq. (62.2); (5) calculate new a = ( P/ p p ); and (6) if new a does not match the assumed a, return to step (3) and repeat the procedure with the new a until convergence. Deflections of rigid pavements under loads are computed by means of Westergaard’s theory [see Eqs. (62.4–62.9)] or more elaborate analysis using the finite-element method. Improved deflection computations using thick-plate theory [Shi et al., 1994; Fwa et al., 1993] could also be used for the purpose of ESWL evaluation. Example 62.7 Calculate the equal subgrade-deflection ESWL for the dual wheels in Example 62.6 for h = 30 in. (h/a) = 4.82. For a point directly below one of the wheels, (r/a)1 = (34/6.22) = 5.47, K1 = 0.15 [from Fig. 62.5(b)]; and (r/a)2 = 0, K2 = 0.31. For the point on the vertical line midway between the two wheels, (r/a)1 = (r/a)2 = 2.73, and K1 = K2 = 0.24 [from Fig. 62.5(b)]. The critical (K1 + K2) = 0.48. The ESWL is obtained by trial and error as follows. The ESWL equals 35,950 lb.
Critical Areas for Pavement Design Trial a
(h/a)
K
ESWL by Eq. (62.10)
New a by Eq. (62.3)
6.5 in. 8.0 in. 7.85 in.
4.615 3.75 3.8217
0.3177 0.3865 0.3797
51,361 lb. 34,704 lb. 35,954 lb.
9.40 7.73 7.86
Runway ends, taxiways, aprons, and turnoff ramp areas receive a concentration of aircraft movements with maximum loads. They are designated as the critical areas for pavement design purposes. Reduced thickness may be used for other areas.
62.5 Thickness Design of Flexible Pavements The thickness design of flexible pavements is a complex engineering problem involving a large number of variables. Most of the design methods in use today are largely empirical or semiempirical procedures derived from either full-scale pavement tests or performance monitoring of in-service pavements. This section presents the methods of the Asphalt Institute and AASHTO for flexible highway pavements and the FAA method for flexible airport pavements. A brief description of the development of the mechanistic approach to flexible pavement design is also presented.
AASHTO Design Procedure for Flexible Highway Pavements The AASHTO design procedure [AASHTO, 1993] was developed based on the findings of the AASHO road test [Highway Research Board, 1962]. It defines pavement performance in terms of the present serviceability index (PSI), which varies from 0 to 5. The PSIs of newly constructed flexible pavements and rigid pavements were found to be about 4.2 and 4.5, respectively. For pavements of major highways, the end of service life is considered to be reached when PSI = 2.5. A terminal value of PSI = 2.0 may be used for secondary roads. Serviceability loss, given by the difference of the initial and terminal serviceability, is required as an input parameter. Pavement layer thicknesses are designed using the nomograph in Fig. 62.6. The design traffic loading in ESAL is computed by Eq. (62.2). Other input parameters are discussed in this section. Reliability The AASHTO guide incorporates in the design a reliability factor R% to account for uncertainties in traffic prediction and pavement performance. R% indicates the probability that the pavement designed will not reach the terminal serviceability level before the end of the design period. The AASHTO suggested
62-24
0
Sta nda Overa ll rd D evia tion ,S
Reliability, R(%)
99.9
.2
99
50
10 5.0 1.0 .5
.4
90 80
.6
.1 .05
TL Design Serviceability Loss, DPSI Effective Roadbed Soil Resilient Modulus, MR (ksi)
TL
Estimated Total 18-kip Equivalent Single Axle Load Applications, W18 (millions)
The Civil Engineering Handbook, Second Edition
40 20 10 5
1 .05
70 60 50
1.0 1.5 2.0 3.0 9 8 7 6
5
4
3
1
2
Design Structural Number, SN
FIGURE 62.6 AASHTO design chart for flexible highway pavements. (Source: AASHTO Guides for Design of Pavement Structures, American Association of State Highway and Transportation Officials, Washington, D.C., 1993. With permission.)
ranges of R% are 85 to 99.9%, 80 to 99%, 80 to 95%, and 50 to 80% for urban interstates, principal arterials, collectors, and local roads, respectively. The corresponding ranges for rural roads are 80 to 99.9%, 75 to 95%, 75 to 95%, and 50 to 80%. The overall standard deviation, so , for flexible and rigid pavements developed at the AASHO road test is 0.45 and 0.35, respectively. Effective Roadbed Soil Resilient Modulus Determination of Subgrade Resilient Modulus. The total pavement thickness requirement is a function of the resilient modulus, Mr , of subgrade soil. Methods for the determination of Mr for granular materials and fine-grained soils are described in AASHTO Test Method T274 [AASHTO, 1989]. Since many laboratories are not equipped to perform the resilient modulus test for soils, it is common practice to estimate Mr through empirical correlation with other soil properties. Equation (62.11) is one such correlation suggested by AASHTO for fine-grained soils with soaked CBR of 10 or less. M r ( psi ) = 1500 ¥ CBR
(62.11)
Other correlations are also found in the literature, such as in the work by Van Til et al. [1972]. Determination of Effective Mr . To account for seasonal variations of subgrade soil resilient modulus, AASHTO defines an effective roadbed soil Mr to represent the combined effect of all the seasonal modulus values. This effective Mr is a weighted value that would give the correct equivalent annual pavement damage for design purpose. The steps in computing the effective Mr are as follows: 1. Divide the year into equal-length time intervals, each equal to the smallest season. AASHTO suggests that the smallest season should not be less than one-half month. 2. Estimate the relative damage uf corresponding to each seasonal modulus by the following equation: u f = 1.18 ¥ 10 ¥ M r 8
– 2.32
(62.12)
where Mr is expressed in 103 psi. 3. Sum the uf of all seasons and divide by the number of seasons to give the average seasonal damage. 4. Substitute the average seasonal damage into Eq. (62.12) and calculate Mr to arrive at the effective roadbed soil Mr .
62-25
Highway and Airport Pavement Design
0.40
1000 800
200 175 150 125 100
4.0 3.0 2.5 2.0
0.20
0.10
900 700 500 300 200 100
3.0 2.5 2.0 1.5
1.0
Modulus-105 psi
5.0 4.5
1300 1100
Marshall stability (1Ib)
1200
300
4.0
1500 Structural coefficient (a2)
1400
6.0
1900 1700
0.30
Modulus(3) 105-psi
0.3
2000 1800 1600
400
Cohesiometer at 140∞
0.4
10.0 9.0 8.0 7.0
Marshall Stability (1Ib)
0.5
Structural layer coefficient
0.6
1.5
600 0.2
400 1.0
(a) Surface Course
(b) Base Course
FIGURE 62.7 Correlation charts for estimating resilient modulus of asphalt concrete. (Source: Van Til, C.J. et al., Evaluation of AASHO Interim Guides for Design of Pavement Structures, NCHRP Report 128, Highway Research Board, Washington, D.C., 1972.)
Example 62.8 This example examines effective roadbed soil resilient modulus. The resilient moduli of a roadbed soil determined at 24 half-month intervals are 6000, 20,000, 20,000, 4000, 4500, 5000, 6000, 6000, 5000, 5000, 5000, 6000, 6000, 6500, 6500, 6500, 6500, 6500, 6000, 6000, 5500, 5500, 5500, and 6000. The total relative damage u computed by Eq. (62.12) is u = 0.2026 + 0.0124 + 0.0124 + 0.5189 + 0.3948 + 0.3092 + 0.2026 + 0.2026 + 0.3092 + 0.3092 + 0.3092 + 0.2026 + 0.2026 + 0.1682 + 0.1682 + 0.1682 + 0.1682 + 0.1682 + 0.2026 + 0.2026 + 0.2479 + 0.2479 + 0.2479 + 0.2026 = 5.568 The mean u = 0.232. Applying Eq. (62.12) again, the effective Mr is 5655 psi. Pavement Layer Modulus Structural thicknesses required above other pavement layers are also determined based on their respective Mr values. For bituminous pavement layers, Mr may be tested by the repeated load indirect tensile test described in ASTM Test D-4123 [ASTM, 1992]. Figure 62.7 shows a chart developed by Van Til et al. [1972] relating Mr of hot-mix asphalt mixtures to other properties. For unbound base and subbase materials, Mr may be estimated from the following correlations: M r ( psi ) = 740 ¥ CBR
for q = 100 psi
(62.13)
62-26
The Civil Engineering Handbook, Second Edition
M r ( psi ) = 440 ¥ CBR
for q = 30 psi
(62.14)
M r ( psi ) = 340 ¥ CBR
for q = 20 psi
(62.15)
M r ( psi ) = 250 ¥ CBR
for q = 10 psi
(62.16)
where q is the sum of principal stresses, (s1 + s 2 + s 3 ). Thickness Requirements Using the input parameters described in the preceding sections, the total pavement thickness requirement is obtained from the nomograph in Fig. 62.6 in terms of structural number SN. SN is an index number equal to the weighted sum of pavement layer thicknesses, as follows: SN = a 1 D 1 + a 2 D 2 m 2 + a 3 D 3 m 3
(62.17)
where a1, a2, and a3 are numbers known as layer coefficients; D1, D2, and D3 are layer thicknesses; and m2 and m3 are layer drainage coefficients. SN can be considered a form of equivalent thickness, and layer coefficients and drainage coefficients are applied to actual pavement thicknesses to account for their structural and drainage properties, respectively. Drainage coefficients are determined from Table 62.10. Coefficient a1 can be estimated from Fig. 62.8. Coefficients a2 and a3 of granular base and subbase layers can be obtained from the following correlations: a 2 = 0.249 ( log 10 M r ) – 0.977
(62.18)
a 3 = 0.227 ( log 10 M r ) – 0.839
(62.19)
where M r = k 1 ( q ) 2 , q is the stress state in psi, and k1 and k2 are regression constants. Recommended values are given in Table 62.11. The thicknesses of individual pavement layers are determined by means of the layer analysis concept depicted in Fig. 62.9. The total structural number required above the subgrade soil, denoted SN1, is k
TABLE 62.10
Base and Subbase Stress States
Asphalt Concrete Thickness (inches)
Roadbed Soil Resilient Modulus (psi) 3000
7500
15,000
(a) Stress State for Base Course Less than 2 2–4 4–6 Greater than 6 Asphalt Concrete Thickness (inches)
201 10 5 5
25 15 10 5
30 20 15 5
Stress State (psi)
(b) Stress State for Subbase (6–12 in.) Less than 2 2–4 Greater than 4
10.0 7.5 5.0
Source: AASHTO Guide for Design of Pavement Structures, American Association of State Highway and Transportation Officials, Washington, D.C., 1993. With permission.
62-27
Highway and Airport Pavement Design
Structural Layer Coefficient a1 for
Asphalt Concrete Surface Course
0.5
0.4
0.3
0.2
0.1
0.0 0
100,000
200,000
300,000
400,000
500,000
Elastic Modulus, EAC (psi), of Asphalt Concrete (at 68∞F)
FIGURE 62.8 Chart for estimating structural layer coefficient of dense-graded asphalt concrete. (Source: AASHTO Guides for Design of Pavement Structures, American Association of State Highway and Transportation Officials, Washington, D.C., 1993. With permission.) TABLE 62.11 Recommended mi Value for Modifying Structural Layer Coefficient of Untreated Base and Subbase Materials in Flexible Pavements Percent of Time Pavement Structure Is Exposed to Moisture Levels Approaching Saturation Quality of Drainage
Less than 1%
1–5%
5–25%
Greater than 25%
Excellent Good Fair Poor Very Poor
1.40–1.35 1.35–1.25 1.25–1.15 1.15–1.05 1.05–0.95
1.35–1.30 1.25–1.15 1.15–1.05 1.05–0.80 0.95–0.75
1.30–1.20 1.15–1.00 1.00–0.80 0.80–0.60 0.75–0.40
1.20 1.00 0.80 0.60 0.40
Source: AASHTO. 1993. AASHTO Guides for Design of Pavement Structures, American Association of State Highway and Transportation Officials, Washington, D.C., 1993. With permission. Design Requirements in Structural Number
SN1 SN2 SN3
Requirements in Layer Thickness
Surface Course
D1
Base Course
D2 a1D1 + a2m2D2 ‡ SN2
Subbase Course
D3
Subgrade
FIGURE 62.9 The concept of layer analysis.
a1D1 ‡ SN1
a1D1 + a2m2D2 + a3m3D3 ‡ SN3
62-28
The Civil Engineering Handbook, Second Edition
determined from the nomograph in Fig. 62.6, with the effective roadbed soil Mr as input. SN2 and SN3 are determined likewise by replacing Mr with E3 (stiffness modulus of subbase material) and E2 (stiffness modulus of base course material), respectively. All pavement layer thicknesses are then derived by solving the following inequalities: SN D 1 ≥ ----------1a1
(62.20)
S N2 – a1 D1 D 2 ≥ --------------------------a2 m2
(62.21)
S N3 – a1 D1 – a2 D2 m2 D 3 ≥ ---------------------------------------------------a3 m3
(62.22)
Environmental Effects The moisture effect on subgrade strength has been considered in the computation of effective roadbed soil Mr . Other environmental impacts such as roadbed swelling, frost heave, aging of asphalt mixtures, and deterioration due to weathering could result in considerable serviceability loss. This loss in serviceability can be added to that caused by traffic loading for design purposes. Minimum Thickness Requirements It is impractical to construct pavement layers less than a certain minimum thickness. AASHTO [1993] recommends minimum thicknesses for different layers as a function of design traffic, which are given in Table 62.12(a). Example 62.9 On the subgrade examined in Example 62.8 is to be constructed a pavement to carry a design lane ESAL of 5 ¥ 106. The elastic moduli of the surface, base, and subbase courses are, respectively, E1 = 360,000, E2 = 30,000, and E3 = 13,000 psi. The drainage coefficients of the base and subbase courses are m2 = 1.20 and m3 = 1.0, respectively. The design reliability is 95% and the standard deviation so is 0.35. Provide a thickness design for the pavement if the initial serviceability level is 4.2 and the terminal serviceability level is 2.5. For R = 95%, so = 0.35, ESAL = 5 ¥ 106, Mr = 5655 psi, and DPSI = 4.2 – 2.5 = 1.7, to obtain SN3 = 5.0 from Fig. 62.6. Repeat the procedure with E3 = 13,000 to obtain SN2 = 3.8, and with E2 = 30,000 to obtain SN1 = 2.7. From Fig. 62.8, a1 = 0.40. By Eq. (62.18), a2 = 0.249(log 30,000) – 0.977 = 0.138, and by Eq. (62.19), a3 = 0.227(log 13,000) – 0.839 = 0.095. The layer thicknesses are D1 = (2.7/0.4) = 6.75 in.; D2 = {3.8 – (0.4 ¥ 6.75)}/(0.138 ¥ 1.20) = 6.64 or 6.75 in.; and D3 = {5.0 – (0.4 ¥ 6.75) – (0.138 ¥ 1.20 ¥ 6.75)}/(0.095 ¥ 1.0) = 12.4 or 12.5 in. TABLE 62.12(a) Minimum Thickness of Pavement Layers — AASHTO Thickness Requirements in Inches Traffic, ESAL Less than 50,000 50,001–150,000 150,001–500,000 500,001–2,000,000 2,000,001–7,000,000 Greater than 7,000,000
Asphalt Concrete
Aggregate Base
1.0 (or surface treatment) 2.0 2.5 3.0 3.5 4.0
4 4 4 6 6 6
Source: AASHTO Guides for Design of Pavement Structures, American Association of State Highway and Transportation Officials, Washington, D.C., 1993. With permission.
62-29
Highway and Airport Pavement Design
TABLE 62.12(b) Asphalt Institute Requirements Traffic, ESAL
Asphalt Concrete Thickness
(a) Minimum Thickness of Asphalt Concrete on Aggregate Base Less than 10,000 Less than 100,000 Greater than 100,000
1 in. (25 mm) 1.5 in. (40 mm) 2 in. (50 mm) Asphalt Concrete Thickness
Traffic, ESAL
Type I Base
Type II and III Base
(b) Minimum Thickness of Asphalt Concrete over Emulsified Asphalt Bases £104 £105 £106 £107 £107
1 in. (25 mm) 1.5 in. (40 mm) 2 in. (50 mm) 2 in. (50 mm) 2 in. (50 mm)
2 in. (50 mm) 2 in. (50 mm) 3 in. (75 mm) 4 in. (100 mm) 5 in. (130 mm)
Source: Asphalt Institute, Asphalt Technology and Construction Practices, Educational Series ES-1, 1983b, p. J25. With permission.
AI Design Procedure for Flexible Highway Pavements The Asphalt Institute [1991] promotes the use of full-depth pavements in which asphalt mixtures are employed for all courses above the subgrade. Potential benefits of full-depth pavements derive from the higher load bearing and spreading capability and moisture resistance of asphalt mixtures as compared to unbound aggregates. Thickness design charts are provided for full-depth pavements, pavements with emulsified asphalt base, and untreated aggregate base. These charts are developed based on two design criteria: (1) maximum tensile strains induced at the underside of the lowest asphalt-bound layer and (2) maximum vertical strains induced at the top of the subgrade layer. The design curves have incorporated the effects of seasonal variations of temperature and moisture on the subgrade and granular base materials. Computation of Design ESAL When detailed vehicle classification and weight data are available, the design lane ESAL is computed according to Eq. (62.2). The AASHTO ESAL factors for SN = 5 and terminal serviceability index = 2.5 are used. When such data are not available, estimates can be made based on the information in Table 62.4. The truck factor in the table refers to the total ESAL contributed by one pass of the truck in question. Example 62.10 Calculate the design lane 20-year ESAL by the AI procedure for a 3-lane rural interstate with an initial directional AADT of 600,000. The predicted traffic growth is 3% per annum and the percent truck traffic is 16%. From Fig. 62.3(b), the design lane is to be designed to carry 80% of the directional truck traffic. Total design lane truck volume = 600,000 ¥ 16% ¥ 80% ¥ {(1 + 0.03)20 – 1}/0.03 = 2,063,645. The total ESAL is computed as follows. Subgrade Resilient Modulus The Asphalt Institute design charts require subgrade resilient modulus Mr as input. However, Mr can be estimated by performing the CBR test [ASTM Method D1883, 1992] or the R-value test [ASTM Method D2844, 1992] and applying the following relationships:
62-30
The Civil Engineering Handbook, Second Edition
M r ( MPa ) = 10.3 CBR
or
M r ( MPa ) = 8.0 + 3.8 R
M r ( psi ) = 1500 CBR
(62.23)
M r = 1155 + 555 R
(62.24)
or
For each soil type, six to eight tests are recommended for the purpose of selecting the design subgrade resilient modulus by the following procedure: (1) arrange all Mr values in ascending order; (2) for each test value, compute y = percent of test values equal to or greater than it; (3) plot y against Mr ; and (4) read from the plot the design subgrade strength at an appropriate percentile value. The design subgrade percentile value is selected according to the magnitude of design ESAL as follows: 60th percentile for ESAL £ 104, 75th percentile if 104 < ESAL < 106, and 87.5th percentile if ESAL ≥ 106. Truck Type SU 2-axle, 4-tire SU 2-axle, 6-tire SU 3-axle or more MU 3-axle MU 4-axle MU 5-axle or more
% Share from Table 62.4(a)
Truck Factor from Table 62.4(b)
39 10 2 1 5 43
0.02 0.19 0.56 0.51 0.62 0.94
ESAL Contribution (Col. 2 ¥ Col. 3)
16,096 29,209 23,113 10,525 63,973 834,125 Total ESAL = 987,041
Example 62.11 Eleven CBR tests on the subgrade for the pavement in Example 62.10 yield the following results: 7, 5, 7, 2, 8, 6, 5, 3, 4, 3, and 6. Determine the design subgrade resilient modulus by the AI method. From Example 62.10, ESAL = 987,041; hence, use the 75th percentile according to the Asphalt Institute recommendation. Next, arrange the test values in ascending order. CBR %≥
2 100
3 91
4 73
5 64
6 45
7 27
8 9
The design CBR (75th-percentile value) is 4%. By Eq. (62.23), the corresponding design M r = 1500 ¥ 4 = 6000 psi. Pavement Thickness Requirements Thickness requirement charts are developed for three different designs of pavement structure: (1) Fig. 62.10 for full-depth pavements, (2) Figs. 62.11–62.13 for pavements with emulsified asphalt base, and (3) Figs. 62.14 and 62.15 for pavements with untreated aggregate base. These charts are valid for mean annual air temperature (MAAT) of 60∞F (15.5∞C). Corresponding charts are also prepared by the Asphalt Institute for MAATs of 45∞F (7∞C) and 75∞F (24∞C). Type I, II, and III emulsified asphalt mixes differ in the aggregates used. Type I mixes are made with processed dense-graded aggregates; type II are made with semiprocessed, crusher-run, pit-run, or bank-run aggregates; and type III are made with sands or silty sands. The minimum thicknesses of full-depth pavements at different traffic levels are indicated in Fig. 62.10. The minimum thicknesses of asphalt concrete surface course for pavements with other base courses are given in Table 62.12(b). Example 62.12 With the data in Examples 62.10 and 62.11, design the required thickness for (1) a full-depth pavement, (2) a pavement with type II emulsified base, and (3) a pavement with 12-in. aggregate base. (1) With ESAL = 987,041 and M r = 6000 psi, the required full-depth pavement thickness is 9.5 in., according to Fig. 62.10. (2) The total required thickness is 11.5 in., from Fig. 62.12. The minimum asphalt concrete surface course is 3 in., according to Table 62.12(b). Hence, the thickness of the emulsified base = 11.5 – 3 = 8.5 in. (3) The required thickness of asphalt concrete is 7.5 in. Use 2 in. of asphalt concrete surface, according to Table 62.12(b), and (7.5 – 2) = 5.5 in. of asphalt base layer.
62-31
Highway and Airport Pavement Design
MAAT = 60°F
Full-Depth Asphalt Concrete
4 2
, 4 in
104
m imu
min
4
5in
2
103 3 10
104
4
2
8in
7in
6in
2
9in
in
10
11 in 12 in 13 in 14 in 15 in 16 17 in i 18 n in 19 in 20 in
Subgrade Resilient Modulus, MR (psi)
105
4 4 2 105 106 2 107 Equivalent 18,000 lb Single Axle Load 4
4
2
8
10
Emulsified Asphalt Mix Type I
105
MAAT = 60°F
4 2
um
inim
,m 4 in
104
103 103
2
4
6in
104
8in
7in
in
9in
10
12 i 13 n in 14 in 15 in 16 17 in i 18 n in 19 in 20 in
5in
2
in
4
11
Subgrade Resilient Modulus, MR (psi)
FIGURE 62.10 Thickness design curves for full-depth asphalt concrete. (Source: Asphalt Institute. 1991. Thickness Design — Asphalt Pavements for Highways and Streets. Manual Series MS-1. With permission.)
4 2 105 106 2 4 Equivalent 18,000 lb Single Axle Load 4
2
107
4
2
108
FIGURE 62.11 Thickness design curves for type I emulsified asphalt mix. (Source: Asphalt Institute. 1991. Thickness Design — Asphalt Pavements for Highways and Streets. Manual Series MS-1. With permission.)
4 2
um inim
,m 4 in
4
10
in
21
4
in
5 in
2
103 3 10
2
4
24
6 in
104
7in
8in
9
in
in
in
10 11
12 in 13 in 14 in 15 in 16 in 17 in 18 in 19i n 20in 22in 23in
Subgrade Resilient Modulus, MR (psi)
MAAT = 60°F
Emulsified Asphalt Type II
105
4 4 105 2 106 2 Equivalent 18,000 lb Single Axle Load
2
4
107
2
4
108
FIGURE 62.12 Thickness design curves for type II emulsified asphalt mix. (Source: Asphalt Institute. 1991. Thickness Design — Asphalt Pavements for Highways and Streets. Manual Series MS-1. With permission.)
62-32
Emulsified Asphalt Type III
105
MAAT = 60°F
4 2
4 in,
um minim in 22 in 4 2
104 5 in 6 in 7in
4 2
103
103
2
in
26
104
4
in n n 10 11i 12i 13in 14in
9in
8in
2
15 in 16 i 17 n in 18 in 19 in 20 i 21 n in 23 in 25 in
Subgrade Resilient Modulus, MR (psi)
The Civil Engineering Handbook, Second Edition
4 4 2 2 105 106 Equivalent 18,000 lb Single Axle Load
107
4
4
2
108
Subgrade Resilient Modulus, MR (psi)
FIGURE 62.13 Thickness design curves for type III emulsified asphalt mix. (Source: Asphalt Institute. 1991. Thickness Design — Asphalt Pavements for Highways and Streets. Manual Series MS-1. With permission.)
Untreated Aggregate Base 6.0 in.
105 4
um m
ini
m
2
104 3 in,
4
2
104
4
imum
, min
um minim
5 in
2
103 103
MAAT = 60°F
4 in
7in
6 in
2
8in
n
10i
9in
n n 11i 12i 13in 4in 5in 6in 1 1 1
4 4 105 2 106 2 Equivalent 18,000 lb Single Axle Load
107
4
2
4
108
Untreated Aggregate Base 12.0 in.
105
MAAT = 60°F
4
um im
in
2
m m
104
,m
4 in
4
imum
3 in, min
6 in
5 in
2
103 103
u inim
2
4
104
2
7in
8in
9in
in 10 11in 12in 3in 1
4 4 105 2 106 2 Equivalent 18,000 lb Single Axle Load 4
14 15 in in
Subgrade Resilient Modulus, MR (psi)
FIGURE 62.14 Thickness design curves for asphalt pavement with 6-in. untreated aggregate base. (Source: Asphalt Institute. 1991. Thickness Design — Asphalt Pavements for Highways and Streets. Manual Series MS-1. With permission.)
107
2
4
108
FIGURE 62.15 Thickness design curves for asphalt pavement with 12-in. untreated aggregate base. (Source: Asphalt Institute. 1991. Thickness Design — Asphalt Pavements for Highways and Streets. Manual Series MS-1. With permission.)
62-33
Highway and Airport Pavement Design
FAA Design Procedure for Flexible Airport Pavements Based on the California bearing ratio (CBR) method of design, FAA [1978] developed — through test track studies and observations of in-service pavements — pavement thicknesses that are necessary to protect pavement layers with various CBR values from shear failure. In establishing the thickness requirements, the equivalent single-wheel loads of wheel assemblies were computed based on deflection consideration. The design assumes that 95% of the gross aircraft weight is carried on the main landing gear assembly and 5% on the nose gear assembly. Generalized design curves are available for single, dual, and dual-tandem main landing gear assemblies. Design curves for specific wide-body aircraft have also been developed. Computation of Design Loading The FAA design charts are based on the equivalent annual departures of a selected design aircraft. The annual departures are assumed to occur over a 20-year life. The following steps are involved in the selection of design aircraft and determination of equivalent annual departures: 1. Obtain forecasts of annual departures by aircraft type. 2. Determine for each aircraft type the required pavement thickness using the appropriate design curve with the forecast number of annual departures for that aircraft. The aircraft requiring the greatest pavement thickness is selected as the design aircraft. 3. Convert the annual departures of all aircraft to equivalent annual departures of the design aircraft by the following formula: 0.5
ÏW ¸ log R eq = log ( R i ¥ F i ) ¥ Ì ------i ˝ ÓW˛
Aircraft 727-100 727-200 707-320B DC-9-30 747-100
where
Single-Wheel Load W i (lbs.)
(R1 ¥ Fi) from Example 62.5
(62.25)
Req by Eq. (62.25)
38,000 4500 2229 45,240 9900 9900 38,830 5440 2890 25,650 5500 655 35,625 102 61 Total equivalent design annual departures = 15,735
Req = equivalent annual departures by the design aircraft Ri = annual departures of aircraft type i Fi = conversion factor obtained from Table 62.9 W = wheel load of the design aircraft Wi = wheel load of aircraft i
In the computation of equivalent annual departures, each wide-body aircraft is treated as a 300,000-lb (136,100-kg) dual-tandem aircraft. Example 62.13 This example entails computation of equivalent annual departures. The equivalent annual departures in design aircraft for the design traffic of Example 62.5 are computed by means of Eq. (62.25), as follows. Pavement Thickness Requirements Figures 62.16–62.22 are the FAA design charts for different aircraft types. The charts have incorporated the effects of load repetitions, landing gear assembly configuration, and the “wandering” (lateral distribution) effect of aircraft movements. With subgrade CBR, gross weight, and total equivalent annual departures of design aircraft as input, the total pavement thickness required can be read from the
62-34
The Civil Engineering Handbook, Second Edition
CBR 3
4
5
6
7
8
9
10
15
20
25
30
40
50
40
50
NOTE CURVES BASED ON 20-YEAR PAVEMENT LIFE THICKNESS - BITUMINOUS SURFACES 4-IN. CRITICAL AREAS 3-IN NONCRITICAL AREAS
GR
OS W SA EI GH IRCR T, A 75 LB FT ,00 0 60 ,00 0 45 ,00 0 30
,00
0
1 in. = 2.54 cm 1 1b. = 0.454 kg
ES
R
1200
TU AR P E
AL
3000
D
6000
U
N
AN
15,000 25,000
3
4
5
6
7
8
9
10
15
20
30
THICKNESS, IN.
FIGURE 62.16 Critical area flexible pavement thickness for single-wheel gear. (Source: Federal Aviation Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C. With permission.)
appropriate chart. Each design chart also indicates the required thickness of bituminous surface course. The minimum base course thickness is obtained from Fig. 62.23. The FAA requires stabilized base and subbase courses to be used to accommodate jet aircraft weighing 100,000 lb or more. These stabilized courses may be substituted for granular courses using the equivalency factors in Table 62.13.
62-35
Highway and Airport Pavement Design
CBR 3
4
5
6
7
8
9 10
15
20
30
40
50
40
50
NOTE: CURVES BASED ON 20-YEAR PAVEMENT LIFE THICKNESS - BITUMINOUS SURFACES 4-IN. CRITICAL AREAS 3-IN. NON CRITICAL AREAS
GR
OS W SA EI G IR 20 HT CRA 0,0 , L F 00 B T 15 0,0 00 10 0,0 00 75 ,00 0
50
,00
0
1 in. = 2.54 cm 1 1b. = 0.454 kg
S
RE
TU AR P E
L
D
1200
A NU
AN
3000 6000 15,000 25,000
3
4
5
6
7
8
9 10
15
20
30
THICKNESS. IN.
FIGURE 62.17 Critical area flexible pavement thickness for dual-wheel gear. (Source: Federal Aviation Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C. With permission.)
The FAA [1978] suggests that the full design thickness T be used at critical areas where departing traffic will be using the pavement, 0.9T be used at areas receiving arriving traffic such as high-speed turnoffs, and 0.7T be used where traffic is unlikely. These reductions in thickness are applied to base and subbase courses. Figure 62.24 shows a typical cross section for runway pavements. For pavements receiving high traffic volumes and exceeding 25,000 departures per annum, the FAA requires that the bituminous surfacing be increased by 1 in. (3 cm) and the total pavement thickness be
62-36
The Civil Engineering Handbook, Second Edition
CBR 3
4
5
6
7
8
9 10
15
20
30
40
50
NOTE: CURVES BASED ON 20-YEAR PAVEMENT LIFE THICKNESS - BITUMINOUS SURFACES 4-IN. CRITICAL AREAS 3-IN NONCRITICAL AREAS
GR
OS W SA E IR 40 IGH CR 0,0 T, A 00 LB FT 30 0,0 00
20
0,0
00
15
0,0
00
10
0,0
00
1 in. = 2.54 cm 1 1b. = 0.454 kg
ES
R TU R A EP
AL
1200
D
3000
U NN
6000
A
15,000 25,000
3
4
5
6
7
8
9 10
15
20
30
40
50
THICKNESS, IN.
FIGURE 62.18 Critical area flexible pavement thickness for dual-tandem gear. (Source: Federal Aviation Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C. With permission.)
increased as follows: 104, 108, 110, and 112% of design thickness (based on 25,000 annual departures) for annual departures of 50,000, 100,000, 150,000, and 200,000, respectively. Example 62.14 For the design traffic in Example 62.13, determine the thickness requirements for a pavement with subgrade CBR = 5 and subbase CBR = 20.
62-37
Highway and Airport Pavement Design
CBR 3
4
5
6
7
8
9 10
15
20
25
30
40
50
NOTE: CURVES BASED ON 20-YEAR PAVEMENT LIFE CONTACT AREA = 245 SQ IN. DUAL SPACING = 44 IN. TANDEM SPACING = 58 IN. THICKNESS - BITUMINOUS SURFACES 5-IN. CRITICAL AREAS 4-IN NONCRITICAL AREAS
GR
O W SS EI AI GH RC 85 T, RA 0, LB FT 0 80 00 70 0,0 0, 00 00 60 0 0, 0 50 00 0, 00 0 40 0,0 00 30 0, 00 0
1 in. = 2.54 cm 1 1b. = 0.454 kg
ES
R
U RT A EP
AL
1200 3000
D
6000
U
N
AN
15,000 25,000
3
4
5
6
7
8
9 10
15
20
30
40
50
THICKNESS, IN.
FIGURE 62.19 Critical area flexible pavement thickness for B-747-100, SR, 200B, 200C, and 200F. (Source: Federal Aviation Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C. With permission.)
The design aircraft has dual-wheel landing gear and a maximum weight of 190,500 lb. Figure 62.17 gives the total thickness requirement as 45 in. above subgrade and 18 in. above subbase. Minimum asphalt concrete surface for the critical area is 4 in. Thickness of base = 18 – 4 = 14 in. Thickness of subbase = 45 – 4 – 14 = 27 in. Since the design aircraft weighs more than 100,000 lb, stabilized base and subbase are needed. Use bituminous base course with equivalency factor of 1.5 [see Table 62.13(a)] and cold-laid
62-38
The Civil Engineering Handbook, Second Edition
CBR 3
4
5
6
7
8
9 10 NOTE:
15
20
25
30
40
50
CURVES ARE BASED ON 20-YEAR PAVEMENT LIFE. CONTACT AREA = 210 SQ IN. DUAL SPACING = 43.25 IN. TANDEM SPACING = 54 IN. THICKNESS - BITUMINOUS SURFACES 5-IN. CRITICAL AREAS 4-IN. NONCRITICAL AREAS
GR
O W SS A EI IR GH C T, RA LB FT 70 0,0 00 60 0, 50 000 0, 00 0 40 0,0 00
ES
R
TU AR P E
AL
D
U
3000 6000
N
AN
1200
15,000 25,000
30
0,0
00
1 in. = 2.54 cm 1 Ib. = 0.454 kg
3
4
5
6
7
8
9 10 15 THICKNESS, IN.
20
30
40
50
FIGURE 62.20 Critical area flexible pavement thickness for B-747-SP. (Source: Federal Aviation Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C. With permission.)
bituminous base course with equivalency factor of 1.5 [see Table 62.13(b)]. The required stabilized base thickness = (14/1.5) = 9 in., and the required subbase thickness = (27/1.5) = 18 in., both for critical areas. In the case of noncritical areas, the asphalt concrete surface thickness is 3 in., and the corresponding base and subbase thicknesses are (9 ¥ 0.9) = 8 in. and (18 ¥ 0.9) = 16 in.
62-39
Highway and Airport Pavement Design
CBR 3
4
5
6
7
8
9 10
15 NOTE:
20
25
30
40
50
CURVES BASED ON 20-YEAR PAVEMENT LIFE CONTACT AREA = 294 SQ IN. DUAL SPACING = 54 IN. TANDEM SPACING = 64 IN. THICKNESS - BITUMINOUS SURFACES 5-IN. CRITICAL AREAS 4-IN. NONCRITICAL AREAS
GR
O W SS A EI IR GH C 45 T, RA LB FT 0,0 00 40 0,0 00 30 0,0 00
20
0,0
00
1 in. = 2.54 cm 1 Ib. = 0.454 kg
ES
UR RT A EP
L
1200 3000
D
A NU
6000
AN
15,000 25,000
3
4
5
6
7
8
9 10 15 THICKNESS, IN.
20
30
40
50
FIGURE 62.21 Critical area flexible pavement thickness for DC 10-10, 10CF. (Source: Federal Aviation Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C. With permission.)
Mechanistic Approach for Flexible Pavement Design The methods described in the preceding sections provide evidence of the continued effort and progress made by engineers toward adopting theoretically sound approaches with fundamental material properties in pavement design. For example, the Asphalt Institute method described is a complete revision that uses
62-40
The Civil Engineering Handbook, Second Edition
CBR 3
4
5
6
7
8
9
10
15 NOTE:
20
25
30
40
50
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
GR
O W SS A EI IR GH C 60 T, RA 0,0 LB FT 0 0
50
0,0
00
40
0,0
00
30
0,0
00
20
0,
00
0
1 in. = 2.54 cm 1 ib. = 0.454 kg
ES
R
U RT A EP
AL
1200
D
3000
U
N
AN
6000 15,000 25,000
3
4
5
6
7
8
9
10
15
20
30
40
50
THICKNESS, IN.
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.)
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
62-41
Highway and Airport Pavement Design
17
20
(cm) 30 35
25
40
45
50
55
100
250
90 80
200
70
175
BR
C E D RA 4
60
BG
130
SU
50 45
120 110
5
40
100 6 90
35
7 80
8
30
9
(cm)
TOTAL PAVEMENT THICKNESS, IN.
150 140
70
10
25
20
12
60
15
50
20
40
15
30
10 6
7
8 9 10 15 20 MINIMUM BASE COURSE THICKNESS, IN.
25
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.)
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 complicated, 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
62-42
The Civil Engineering Handbook, Second Edition
TABLE 62.13 FAA-Recommended Equivalency Factors for Stabilized Base and Subbase Equivalency Factor
Material
(a) Equivalency Factors for Stabilized Base Course Bituminous surface course Bituminous base course Cold-laid bituminous base course Mixed-in-place base course Cement-treated base course Soil cement base course Crushed aggregate base course Subbase course
1.2–1.6 1.2–1.6 1.0–1.2 1.0–1.2 1.2–1.6 N/A 1.0 N/A
(b) Equivalency Factors for Stabilized Subbase Course Bituminous surface course Bituminous base course Cold-laid bituminous base course Mixed-in-place base course Cement-treated base course Soil cement base course Crushed aggregate base course Subbase course
1.7–2.3 1.7–2.3 1.5–1.7 1.5–1.7 1.6–2.3 1.5–2.0 1.4–2.0 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.
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 relationships 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 Ec and modulus of rupture Sc of concrete are required input parameters. Ec is determined by the procedure specified in ASTM C469. It could also be estimated using the following correlation recommended by ACI [1977]: E c ( psi ) = 57,000 ( f c )
0.5
(62.26)
where fc = the concrete compressive strength in psi as determined by AASHTO T22, T140 [AASHTO, 1989] or ASTM C39 [ASTM, 1992].
62-43
Highway and Airport Pavement Design
200’ (61m)
200’ (61m)
P1
200’ (61m)
A
200’ (61m)
P1 A TRANSITIONS
TRANSITIONS
NOTES
RUNWAY WIDTH 1 2"(1 cm) MINIMUM SURFACE THICKNESS
SURFACE
3
1 RUNWAY WIDTHS IN ACCORDANCE WITH APPLICABLE ADVISORY CIRCULAR.
2 BASE
2 TRANSVERSE SLOPES IN ACCORDANCE WITH APPLICABLE ADVISORY CIRCULAR.
PCC
SUBBASE
3 SURFACE, BASE, PCC, ETC., THICKNESS AS INDICATED ON DESIGN CHART.
SUBBASE
4
4 5
200’ (61m)
5
6@ 25’ (7.6 m)
4 MINIMUM 12" (30 cm) UP TO 30" (90cm) ALLOWABLE. 5 FOR RUNWAYS WIDER THAN 150’ (45.7 m) THIS DIMENSION WILL INCREASE.
LEGEND THICKNESS = T THICKNESS TAPERS = T
O.7 T
THICKNESS = 0.9 T THICKNESS = 0.7 T
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.)
Sc 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 Mr . 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 DSB = 6 in., ESB = 20,000 psi, and Mr = 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 Mr 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 Mr , except that the relative damage u is now computed as u = (D
0.75
– 0.39k
0.25 3.42
)
Instead of solving the above equation, u can be obtained from Fig. 62.27.
(62.27)
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The Civil Engineering Handbook, Second Edition
1,000,000 600,000 400,000 200,000 100,000 75,000 50,000 30,000 15,000
Composite Modulus of Subgrade Reaction, k•(pci) (Assumes Semi— infinite Subgrade 20 Depth) 15 00 0 10 0 8 00 60 00 5 0 4 00 30 00 0 20 0
Subbase Elastic Modulus, ESB (psi)
10
0
50
Subbase Thickness, DSB (inches) 1000
18
16
14
12
10
8
6
2000 3000
ur (T ng
ni
5000 7000 10,000 12,000 16,000 20,000
)
ne
Li
Roadbed Soil Resilient Modulus, MR (psi)
FIGURE 62.25 Chart for estimating composite k •. (Source: AASHTO. 1993. AASHTO Guides for Design of Pavement Structures. Copyright 1993 by the American Association of State Highway and Transportation Officials, Washington, D.C. Used by permission.)
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 movements. 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
62-45
Highway and Airport Pavement Design
Modulus of Subgrade Reaction, k•(pci) Assuming Semi-infinite Subgrade Depth 50 100
200
300
400
Subgrade Depth to Rigid Foundation, DSG (ft.) 500
600
700 800 2 5
1000
10
1200 1400 20,000
15,000
10,000
5,000
Roadbed Soil Resilient Modulus, MR (psi)
0
500
1000
1500
2000
Modulus of Subgrade Reaction, k (pci) (Modified to account for presence of rigid foundation near surface)
FIGURE 62.26 Chart for k as a function of bedrock depth. (Source: AASHTO. 1993. AASHTO Guides for Design of Pavement Structures. Copyright 1993 by the American Association of State Highway and Transportation Officials, Washington, D.C. Used by permission.)
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 Cd was included in the design. Setting Cd = 1 for conditions at the AASHO road test, Table 62.16 shows the Cd 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 ¥ 106. 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 Ec = 5 ¥ 106, S c¢ = 650 psi, J = 3.2, and Cd = 1.0. Design PSI loss = 4.5 – 2.5 = 2.0. From Fig. 62.29, D = 10 in.
62-46
The Civil Engineering Handbook, Second Edition
1000 14 500 12 Projected Slab Thickness (inches)
10 9 8
100
Relative Damage, u
7 50
6
Projected Slab Thickness (inches)
10
5
1 10
50
100
500
1000
2000
Composite k-value (pci)
FIGURE 62.27 Chart for estimating relative damage to rigid pavements. (Source: AASHTO. 1993. AASHTO Guides for Design of Pavement Structures. Copyright 1993 by the American Association of State Highway and Transportation Officials, Washington, D.C. Used by permission.)
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 relatively 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 L◊F P s = ---------- ¥ 100% 2f s
(62.28)
62-47
Highway and Airport Pavement Design
Effective Modulus of Subgrade Reaction, K (pci) (Corrected for Potential Loss of Support)
1000 500
(170) 100 50 =0
LS
10
0
1.
= LS
.0
=2
LS 5
.0
=3
LS
(540) 1 5
10
50
100
500 1000 2000
Effective Modulus of Subgrade Reaction, K (pci)
FIGURE 62.28 Correction of effective modulus of subgrade reaction for potential loss of subbase support. (Source: AASHTO. 1993. AASHTO Guides for Design of Pavement Structures. Copyright 1993 by the American Association of 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 Cement treatment granular base (E = 1,000,000 to 2,000,000 psi) Cement aggregate mixtures (E = 500,000 to 1,000,000 psi) Asphalt treated base (E = 350,000 to 1,000,000 psi) Bituminous stabilized mixtures (E = 40,000 to 300,000 psi) Lime stabilized (E = 20,000 to 70,000 psi) Unbound granular materials (E = 15,000 to 45,000 psi) Fine-grained or natural subgrade materials (E = 3000 to 40,000 psi)
Loss of Support (LS) 0.0–1.0 0.0–1.0 0.0–1.0 0.0–1.0 1.0–3.0 1.0–3.0 2.0–3.0
Source: AASHTO. 1993. AASHTO Guides for Design of Pavement Structures. Copyright 1993 by the American Association of State Highway and Transportation Officials, Washington, D.C. Used by permission.
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 fs = 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, fs is equal to 30,000 and 45,000 psi, respectively. For welded wire fabric, fs is 48,750 psi. Equation (62.28) is also applicable to the design of transverse steel reinforcement for continuously reinforced concrete pavement (CRCP).
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The Civil Engineering Handbook, Second Edition
TABLE 62.15 Recommended Load Transfer Coefficient for Various Pavement Types and Design Conditions Shoulder
Asphalt
Load Transfer Device
Tied P.C.C.
Yes
No
Yes
No
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
Pavement Type
Source: AASHTO. 1993. AASHTO Guides for Design of Pavement Structures. Copyright 1993 by the American Association of State Highway and Transportation Officials, Washington, D.C. Used by permission.
TABLE 62.16 Recommended Value of Drainage Coefficient, Cd , for Rigid Pavement Design Percent of Time Pavement Structure Is Exposed to Moisture Levels Approaching Saturation Quality of Drainage
Less than 1%
1–5%
5–25%
Greater than 25%
Excellent Good Fair Poor Very Poor
1.25–1.20 1.20–1.15 1.15–1.10 1.10–1.00 1.00–0.90
1.20–1.15 1.15–1.10 1.10–1.00 1.00–0.90 0.90–0.80
1.15–1.10 1.10–1.00 1.00–0.90 0.90–0.80 0.80–0.70
1.10 1.00 0.90 0.80 0.70
Source: AASHTO. 1993. AASHTO Guides for Design of Pavement Structures. Copyright 1993 by the American Association of State Highway and Transportation Officials, Washington, D.C. Used by permission.
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 Ps = (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: (Pmin )1 and (Pmax )1. The amount of steel reinforcement 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: (Pmax)1 and (Pmin)1. The input variables for determining P are the thermal coefficient of portland cement concrete ac, the thermal coefficient of steel as, diameter of reinforcing bar, concrete shrinkage Z at 28 days, tensile stress sw due to wheel load, and concrete tensile strength ft at 28 days. Values of a c and Z are given in Table 62.18. A value of a s = 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, sw is the tensile stress developed during initial loading of the constructed pavement by either construction
62-49
Highway and Airport Pavement Design
Design slab thickness, D (inches)
0
700 600 500 800 500
100
50
10
2.5 2.2
1.3 1.1 0.9 0.7 0.6
40 50 60 70
Design Serviceability Loss, ∆PSI
800
30 Match Line
900
20 4.5 4.0 3.5 3.0
Drainage Coefficient, Cd
1000
10
TL
TL
Load Transfer Coefficient, J
1200 1100
7 6 5 4 3
Mean Concrete Modulus of Rupture, S′c (psi)
Concrete Elastic Modulus, Ec(106pci)
14 13 12 11 10 9
8
7
6
55
.5 1.0 2.0 3.0
80 Estimated Total 18−kip Equivalent Single Axle Load (ESAL) Applications, W8 (millions)
90
Effective Modulus of Subgrade Reaction, k (pci)
1000 500
100
100 50
10
5
10 5
1 05
NOTE : Application of reliablility in this chart requires the use of mean values for all the input variables.
TL
Ove
2
rall
99.9
3 dard
Stan
4 5 6 Dev iatio n,
99
95 90
S
0
80 70 60 50
Reliability, R (%)
FIGURE 62.29 Rigid pavement thickness design chart. (Source: AASHTO. 1993. AASHTO Guides for Design of Pavement Structures. Copyright 1993 by the American Association of State Highway and Transportation Officials, Washington, D.C. Used by permission.)
TABLE 62.17 Recommended Friction Factors Type of Material beneath Slab
Friction Factor
Surface treatment Lime stabilization Asphalt stabilization Cement stabilization River gravel Crushed stone Sandstone Natural subgrade
2.2 1.8 1.8 1.8 1.5 1.5 1.2 0.9
Source: AASHTO. 1993. AASHTO Guides for Design of Pavement Structures. Copyright 1993 by the American Association of State Highway and Transportation Officials, Washington, D.C. Used by permission.
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, ft is the concrete indirect tensile strength determined by AASHTO T198 or ASTM C496. It can be assumed as 86% of the modulus of rupture Sc used for thickness design. CRCP Reinforcements Based on Crack Width: (Pmin )2. Crack width in CRCP is controlled to within 0.04 in. (1.0 mm) to prevent spalling and water infiltration. The minimum percent steel (Pmin)2 that would produce crack widths of 0.04 in. can be determined from Fig. 62.32 with a selected bar size and input variables sw and ft .
62-50
12.0 11.0 10.0 9.0
Undesirable
The Civil Engineering Handbook, Second Edition
TL
TL
TL
TL
.9
.75 .50
5/8 3/4
2.0
Undesirable
3.0
.0002 .0004 .0006 .0008
200
800 700
160 120
600
80 500
400
.8
Percent Steel, P
1.00
1/2
280 240
Concrete Tensile Strength at 28 Days, ft (psi)
4.0
2.0 1.50
Tensile Stress Due to Wheel Load, sw(psi)
5.0
Bar Diameter, f (in.)
6.0
as/ac Ratio
Crack Spacing, X (ft.)
7.0
Concrete Shrinkage at 28 Days, Z (in./in.)
8.0
.7
.6
.5
.4
FIGURE 62.30 Minimum percent reinforcement to satisfy crack-spacing criteria. (Source: AASHTO. 1993. AASHTO Guides for Design of Pavement Structures. Copyright 1993 by the American Association of State Highway and Transportation Officials, Washington, D.C. Used by permission.) TABLE 62.18 Shrinkage and Thermal Coefficient of Portland Cement Concrete Indirect Tensile Strength (psi)
Shrinkage (in./in.)
(a) Approximate Relations between Shrinkage and Indirect Tensile Strength of Portland Cement Concrete 300 (or less) 400 500 600 700 (or greater)
0.0008 0.0006 0.00045 0.0003 0.0002
Type of Coarse Aggregate
Concrete Thermal Coefficient (10–6/˚F)
(b) Recommended Value of the Thermal Coefficient of Concrete as a Function of Aggregate Types Quartz Sandstone Gravel Granite Basalt Limestone
6.6 6.5 6.0 5.3 4.8 3.8
Source: AASHTO. 1993. AASHTO Guides for Design of Pavement Structures. Copyright 1993 by the American Association of State Highway and Transportation Officials, Washington, D.C. Used by permission.
62-51
Highway and Airport Pavement Design
600
13
24 ,0 00
22
12
WHEEL LOAD MAGNITUDE (POUNDS)
EFFECTIVE MODULUS OF SUBGRADE REACTION k (pci)
550
0 ,0 50
0 00
,0
20 18
11
100
,0
00
500
16
,0
00 20 0
,0
00
12
,0
400
10
40
0
300
00
9
,0
8
00 0
8,0
00
7
350
6,0
Wheel Load Tensile Stress σw (psi)
450
14
50
Design Slab Thickness, D (inches)
10
300
00
EXAMPLE: 6
5
250
D = 9.5 in. WHEEL LOAD = 20,000 lb. k = 170 pci SOLUTION: σw = 230 psi
200
150
4
FIGURE 62.31 Chart for estimating wheel load tensile stress s w . (Source: AASHTO. 1993. AASHTO Guides for Design of Pavement Structures. Copyright 1993 by the American Association of State Highway and Transportation Officials, Washington, D.C. Used by permission.)
CRCP Reinforcements Based on Steel Stress: (Pmin )3 . To guard against steel fracture and excessive permanent deformation, a minimum amount of steel (Pmin)3 is determined according to Fig. 62.33. Input variables Z, sw , and ft have been determined earlier. For the steel stress ss , a limiting value equal to 75% of the ultimate tensile strength is recommended. Table 62.19 gives the allowable steel working stress for grade 60 steel meeting ASTM A615 specifications. The determination of (Pmin)3 also requires the computation of a design temperature drop given by DT D = T H – T L where
(62.29)
TH = the average daily high temperature during the month the pavement is constructed TL = the average daily low temperature during the coldest month of the year
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The Civil Engineering Handbook, Second Edition
.05 .04 .03
Bar Diameter, f (in.)
Crack Width, CW (in.)
.06
3/4 5/8 1/2
.02
TL
.9
280
.8
800
240 200 160 120 80
700
600
Percent Steel, P
Tensile Stress Due to Wheel Load, sw (psi)
TL
Concrete Tensile Strength, ft (psi)
.10 .09 .08 .07
.7
.6
.5
500
.4 400
.01
FIGURE 62.32 Minimum percent steel reinforcement to satisfy crack-width criteria. (Source: AASHTO. 1993. AASHTO Guides for Design of Pavement Structures. Copyright 1993 by the American Association of State Highway and Transportation Officials, Washington, D.C. Used by permission.)
20
60 70
90 100 110
Undesirable
80
45 65 100
300 220 140 60
.8 800 700 600 500
.7
.6
Percent Steel, P
35 55 75
.0002 .0005 .0008
.9 Concrete Tensile Strength, ft (psi)
50
TL
Tensile Stress Due to Wheel Load, σW (psi)
Design Temperature Drop, DTD (°F)
Steel Stress, σs (ksi)
40
TL
- (in/in) Concrete Shrinkage at 28 Days, Z
TL
30
.5
400 .4
120
FIGURE 62.33 Minimum percent reinforcement to satisfy steel–stress criteria. (Source: AASHTO 1993. AASHTO Guides for Design of Pavement Structures. Copyright 1993 by the American Association of State Highway and Transportation Officials, Washington, D.C. Used by permission.)
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Highway and Airport Pavement Design
TABLE 62.19
Allowable Steel Working Stress, ksi Reinforcing Bar Size
Indirect Tensile Strength of Concrete at 28 days, psi
No. 4
No. 5
No. 6
300 (or less) 400 500 600 700 800 (or greater)
65 67 67 67 67 67
57 60 61 63 65 67
54 55 56 58 59 60
Source: AASHTO. 1993. AASHTO Guides for Design of Pavement Structures. Copyright 1993 by the American Association of State Highway and Transportation Officials, Washington, D.C. Used by permission.
Reinforcement Design. Based on the three criteria discussed above, the design percent steel should fall within Pmax and Pmin given by P max = ( P max ) 1
(62.30)
P min = max { ( P min ) 1, ( P min ) 2, ( P min ) 3 }
(62.31)
If Pmax is less than Pmin, a design revised by changing some of the input parameters is required. With Pmax greater than Pmin, the number of reinforcing bars or wires required, N, is given by Nmin £ N £ Nmax , where Nmin and Nmax are computed by N min = 0.01273P min Ws D § f
2
N max = 0.01273P max W s D § f where
2
(62.32) (62.33)
Ws = the width of pavement in inches D = the slab thickness in inches f = the reinforcing bar or wire diameter in inches
Example 62.19 This example concerns longitudinal steel reinforcement design for CRCP. Design data are D = 9 in., as = 5 ¥ 10–6 in./in./˚F, ac = 5.3 ¥ 10–6 for concrete with granite coarse aggregate (see Table 62.18), ft = 600 psi at 28 days, Z = 0.0003 (see Table 62.18), maximum construction wheel load = 18,000 lb, effective k = 100 pci, and design temperature drop = 55˚F. Try steel bar diameter f = 0.5 in. (a) Crack spacing control. sw = 240 psi, from Fig. 62.31. With (as /ac) = 0.94, obtain (Pmin)1 < 0.4% for X = 8 ft, and (Pmax)2 = 0.49% for X = 3.5 ft from Fig. 62.30. (b) Crack width control. Obtain (Pmin)2 = 0.40% from Fig. 62.32. (c) Steel stress control. ss = 67 psi, from Table 62.19. Obtain (Pmin)3 = 0.45%. Hence, overall (Pmin) = 0.4% and (Pmax) = 0.49%. For a pavement width of 12 ft, apply Eqs. (62.32) and (62.33), Nmin = 29.7, Nmax = 32.3. Use 30 numbers of 0.5-in. bars.
PCA Thickness Design Procedure for Rigid Highway Pavements The thickness design procedure published by PCA [1984] was developed by relating theoretically computed values of stress, deflection, and pressure to pavement performance criteria derived from data of (1) major road test programs, (2) model and full-scale tests, and (3) performance of normally constructed pavements subject to normal mixed traffic. Traffic-loading data in terms of axle load distribution are obtained in the usual way as described earlier in this chapter. Each axle load is further multiplied by a load safety factor (LSF) according to the following recommendations: (1) LSF = 1.2 for interstate highways and other multilane projects with uninterrupted
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The Civil Engineering Handbook, Second Edition
traffic flow and high volumes of truck traffic; (2) LSF = 1.1 for highways and arterial streets with moderate volumes of truck traffic; and (3) LSF = 1.0 for roads, residential streets, and other streets with small volumes of truck traffic. The flexural strength of concrete is determined by the 28-day modulus of rupture from third-point loading according to ASTM Test Method C78. Subgrade and subbase support is defined in terms of the modulus of subgrade reaction k. The design procedure consists of a fatigue analysis and an erosion analysis, which are considered separately using different sets of tables and design charts. The final thickness selected must satisfy both analyses. Fatigue Design Fatigue design is performed with the aim to control fatigue cracking. The slab thickness based on fatigue design is the same for JRCP, for JPCP with doweled and undoweled joints, and for CRCP. This is because the most critical loading position is near midslab and the effect of joints is negligible. The presence of a tied concrete shoulder, however, must be considered since it significantly reduces the critical edge stress. The analysis is based on the concept of cumulative damage given by D = where
m
n
 -----i i = 1 Ni
(62.34)
m = the total number of axle load groups ni = the predicted number of repetitions for the ith load group Ni = the allowable number of repetitions for the ith load group
The steps in the design procedure are: 1. Multiply the load of each design axle load group by the appropriate LSF. 2. Assume a trial slab thickness. 3. Obtain from Table 62.20(a) or (b) the equivalent stress for the input slab thickness and k, and calculate the stress ratio factor as Equivalent stress Stress ratio factor = -------------------------------------------------------------Concrete flexural strength
(62.35)
4. For each axle load i, obtain from Fig. 62.34 the allowable load repetitions Ni. 5. Compute D from Eq. (62.34). If D exceeds 1, select a greater trial thickness and repeat steps 3 through 5. The trial thickness is adequate if D is less than or equal to 1. Erosion Design PCA requires erosion analysis in pavement thickness design to control foundation and shoulder erosion, pumping, and faulting. Since the most critical deflection occurs at the corner, the presence of shoulder and the type of joint construction will both affect the analysis. The concept of cumulative damage as defined by Eq. (62.34) is again applied. The steps are: 1. 2. 3. 4. 5.
Multiply the load of each design axle load group by the LSF. Assume a trial slab thickness. Obtain from Table 62.21(a), (b), (c), or (d) the erosion factor for the input slab thickness and k. For each axle load i, obtain from Fig. 62.35(a) or (b) the allowable load repetitions Ni. Compute D from Eq. (62.34). If D exceeds 1, select a greater trial thickness and repeat steps 3 through 5. The trial thickness is adequate if D is less than or equal to 1.
Example 62.20 Determine the required slab thickness for an expressway with the design traffic shown in the table below. The pavement is to be constructed with doweled joint but without concrete shoulder. Concrete modulus of rupture is 650 psi. The subgrade k is 130 pci.
62-55
Highway and Airport Pavement Design
TABLE 62.20 Slab Thickness (in.)
Equivalent Stress for Fatigue Analysis k of Subgrade–Subbase (pci) 50
100
150
200
300
500
700
(a) Equivalent Stress — No Concrete Shoulder (Single Axle/Tandem Axle) 4 in. 4.5 in. 5 in. 5.5 in. 6 in. 6.5 in. 7 in. 7.5 in. 8 in. 8.5 in. 9 in. 9.5 in. 10 in. 10.5 in. 11 in. 11.5 in. 12 in. 12.5 in. 13 in. 13.5 in. 14 in.
825/679 699/586 602/516 526/461 465/416 417/380 375/349 340/323 311/300 285/281 264/264 245/248 228/235 213/222 200/211 188/201 177/192 168/183 159/176 152/168 144/162
726/585 616/500 531/436 464/387 411/348 367/317 331/290 300/268 274/249 252/232 232/218 215/205 200/193 187/183 175/174 165/165 155/158 147/151 139/144 132/138 125/133
671/542 571/460 493/399 431/353 382/316 341/286 307/262 279/241 255/223 234/208 216/195 200/183 186/173 174/164 163/155 153/148 144/141 136/135 129/129 122/123 116/118
634/516 540/435 467/374 409/331 362/296 324/267 292/244 265/224 242/208 222/193 205/181 190/170 177/160 165/151 154/143 145/136 137/130 129/124 122/119 116/114 110/109
584/486 498/406 432/349 379/305 336/271 300/244 271/222 246/203 225/188 206/174 190/163 176/153 164/144 153/136 144/129 135/122 127/116 120/111 113/106 107/102 102/98
523/457 448/378 390/321 343/278 304/246 273/220 246/199 224/181 205/167 188/154 174/144 161/134 150/126 140/119 131/113 123/107 116/102 109/97 103/93 98/89 93/85
484/443 417/363 363/307 320/264 285/232 256/207 231/186 210/169 192/155 177/143 163/133 151/124 141/117 132/110 123/104 116/98 109/93 103/89 97/85 92/81 88/78
(b) Equivalent Stress — Concrete Shoulder (Single Axle/Tandem Axle) 4 in. 4.5 in. 5 in. 5.5 in. 6 in. 6.5 in. 7 in. 7.5 in. 8 in. 8.5 in. 9 in. 9.5 in. 10 in. 10.5 in. 11 in. 11.5 in. 12 in. 12.5 in. 13 in. 13.5 in. 14 in.
640/534 547/461 475/404 418/360 372/325 334/295 302/270 275/250 252/232 232/216 215/202 200/190 186/179 174/170 164/161 154/153 145/146 137/139 130/133 124/127 118/122
559/468 479/400 417/349 368/309 327/277 294/251 266/230 243/211 222/196 205/182 190/171 176/160 164/151 154/143 144/135 136/128 128/122 121/117 115/112 109/107 104/103
517/439 444/372 387/323 342/285 304/255 274/230 248/210 226/193 207/179 191/166 177/155 164/146 153/137 144/130 135/123 127/117 120/111 113/106 107/101 102/97 97/93
489/422 421/356 367/308 324/271 289/241 260/218 236/198 215/182 197/168 182/156 169/146 157/137 146/129 137/121 129/115 121/109 114/104 108/99 102/95 97/91 93/87
452/403 390/338 341/290 302/254 270/225 243/203 220/184 201/168 185/155 170/144 158/134 147/126 137/118 128/111 120/105 113/100 107/95 101/91 96/86 91/83 87/79
409/388 355/322 311/274 276/238 247/210 223/188 203/170 185/155 170/142 157/131 146/122 136/114 127/107 119/101 112/95 105/90 99/86 94/82 89/78 85/74 81/71
383/384 333/316 294/267 261/231 234/203 212/180 192/162 176/148 162/135 150/125 139/116 129/108 121/101 113/95 106/90 100/85 95/81 90/77 85/73 81/70 77/67
Source: Portland Cement Association. 1984. Thickness Design for Concrete Highway and Street Pavements. With permission.
A trial-and-error approach is needed by assuming slab thickness. The solution is shown only for slab thickness h = 9.5 in. For an expressway, the LSF = 1.2. The design load is equal to (1.2 ¥ axle load). From Table 62.20, equivalent stress for single axle is 206 and for tandem axle is 192. The corresponding stress ratios are
62-56
The Civil Engineering Handbook, Second Edition
SINGLE AXLE LOAD, KIPS 60
58
56
54
52
48
50
46
44
42
40
38
36
34
32
28
30
26
24
22
20
18
120
110
100
90
80
70
60
50
40
30
20
16
16
14
10
12
8
ESS
O FA CTO
0.20
RATI
0.25
STR
0.30
0.40
0.50
0.60
0.70
0.80 0.90 1.00
1.50
TANDEM AXLE LOAD, KIPS
R
0.15 10,000,000
6 4 2
1,000,000
8 6 4
2
8
100,000
6
4
2
8
10,000
6
4
2
8
1000
6
4
2
100
ALLOWABLE LOAD REPETITIONS
FIGURE 62.34 Allowable repetitions for fatigue analysis. (Source: Portland Cement Association. 1984. Thickness Design for Concrete Highway and Street Pavements, p. 15. With permission.)
0.317 and 0.295. N1 for fatigue analysis is obtained from Fig. 62.34. From Table 62.21, the erosion factor is 2.6 for single axle and is 2.8 for tandem axle. N2 for erosion analysis is obtained from Fig. 62.35(a). The results show that the design is satisfactory. Axle Load (kips)
Design Load (kips)
Design n
52T 50T 48T 46T 44T 42T 40T 30S 28S 26S 24S 22S
62.4T 60.0T 57.6T 55.2T 52.8T 50.4T 48.0T 36.0S 33.6S 31.2S 28.8S 26.4S
3,100 32,000 32,000 48,000 158,000 172,000 250,000 3,100 3,100 9,300 545,000 640,000
Fatigue N1 800,000 2,000,000 10,000,000 Unlimited Unlimited Unlimited Unlimited 25,000 70,000 200,000 800,000 10,000,000 Total
Erosion (n/N1)
N2
(n/N2)
0.004 0.016 0.0032 0 0 0 0 0.124 0.044 0.045 0.682 0.064 0.982
800,000 1,000,000 1,200,000 1,700,000 2,000,000 2,800,000 3,500,000 1,700,000 2,200,000 3,000,000 5,000,000 9,000,000
0.004 0.030 0.027 0.028 0.079 0.061 0.071 0.002 0.001 0.002 0.033 0.071 0.41
FAA Method for Rigid Airport Pavement Design Both the thickness design and reinforcement design procedures by the FAA [1978] are presented in this section.
62-57
Highway and Airport Pavement Design
TABLE 62.21 Slab Thickness (in.)
Erosion Factors for Erosion Analysis k of Subgrade–Subbase (pci) 50
100
200
300
500
700
(a) Erosion Factors — Doweled Joints, No Concrete Shoulder (Single Axle/Tandem Axle) 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14
3.74/3.83 3.59/3.70 3.45/3.58 3.33/3.47 3.22/3.38 3.11/3.29 3.02/3.21 2.93/3.14 2.85/3.07 2.77/3.01 2.70/2.96 2.63/2.90 2.56/2.85 2.50/2.81 2.44/2.76 2.38/2.72 2.33/2.68 2.28/2.64 2.23/2.61 2.18/2.57 2.13/2.54
3.73/3.79 3.57/3.65 3.43/3.52 3.31/3.41 3.19/3.31 3.09/3.22 2.99/3.14 2.91/3.06 2.82/2.99 2.74/2.93 2.67/2.87 2.60/2.81 2.54/2.76 2.47/2.71 2.42/2.67 2.36/2.62 2.30/2.58 2.25/2.54 2.20/2.50 2.15/2.47 2.11/2.43
3.72/3.75 3.56/3.61 3.42/3.48 3.29/3.36 3.18/3.26 3.07/3.16 2.97/3.08 2.88/3.00 2.80/2.93 2.72/2.86 2.65/2.80 2.58/2.74 2.51/2.68 2.45/2.63 2.39/2.58 2.33/2.54 2.28/2.49 2.23/2.45 2.18/2.41 2.13/2.37 2.08/2.34
3.71/3.73 3.55/3.58 3.41/3.45 3.28/3.33 3.17/3.23 3.06/3.13 2.96/3.05 2.87/2.97 2.79/2.89 2.71/2.82 2.63/2.76 2.56/2.70 2.50/2.64 2.44/2.59 2.38/2.54 2.32/2.49 2.26/2.44 2.21/2.40 2.16/2.36 2.11/2.32 2.07/2.29
3.70/3.70 3.54/3.55 3.40/3.42 3.27/3.30 3.15/3.20 3.05/3.10 2.95/3.01 2.86/2.93 2.77/2.85 2.69/2.78 2.62/2.71 2.55/2.65 2.48/2.59 2.42/2.54 2.36/2.49 2.30/2.44 2.25/2.39 2.19/2.35 2.14/2.30 2.09/2.26 2.05/2.23
3.68/3.67 3.52/3.53 3.38/3.40 3.26/3.28 3.14/3.17 3.03/3.07 2.94/2.98 2.84/2.90 2.76/2.82 2.68/2.75 2.61/2.68 2.54/2.62 2.47/2.56 2.41/2.51 2.35/2.45 2.29/2.40 2.23/2.36 2.18/2.31 2.13/2.27 2.08/2.23 2.03/2.19
(b) Erosion Factors — Aggregate–Interlock Joints, No Concrete Shoulder (Single Axle/Tandem Axle) 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14
3.94/4.03 3.79/3.91 3.66/3.81 3.54/3.72 3.44/3.64 3.34/3.56 3.26/3.49 3.18/3.43 3.11/3.37 3.04/3.32 2.98/3.27 2.92/3.22 2.86/3.18 2.81/3.14 2.77/3.10 2.72/3.06 2.68/3.03 2.64/2.99 2.60/2.96 2.56/2.93 2.53/2.90
3.91/3.95 3.76/3.82 3.63/3.72 3.51/3.62 3.40/3.53 3.30/3.46 3.21/3.39 3.13/3.32 3.05/3.26 2.98/3.21 2.91/3.16 2.85/3.11 2.79/3.06 2.74/3.02 2.69/2.98 2.64/2.94 2.60/2.90 2.55/2.87 2.51/2.83 2.47/2.80 2.44/2.77
3.88/3.89 3.73/3.75 3.60/3.64 3.48/3.53 3.37/3.44 3.26/3.36 3.17/3.29 3.09/3.22 3.01/3.16 2.93/3.10 2.86/3.05 2.80/3.00 2.74/2.95 2.68/2.91 2.63/2.86 2.58/2.82 2.53/2.78 2.48/2.75 2.44/2.71 2.40/2.68 2.36/2.65
3.86/3.86 3.71/3.72 3.58/3.60 3.46/3.49 3.35/3.40 3.25/3.31 3.15/3.24 3.07/3.17 2.99/3.10 2.91/3.04 2.84/2.99 2.77/2.94 2.71/2.89 2.65/2.84 2.60/2.80 2.55/2.76 2.50/2.72 2.45/2.68 2.40/2.65 2.36/2.61 2.32/2.58
3.82/3.83 3.68/3.68 3.55/3.55 3.43/3.44 3.32/3.34 3.22/3.25 3.13/3.17 3.04/3.10 2.96/3.03 2.88/2.97 2.81/2.92 2.75/2.86 2.68/2.81 2.62/2.76 2.57/2.72 2.51/2.68 2.46/2.64 2.41/2.60 2.36/2.56 2.32/2.53 2.28/2.50
3.77/3.80 3.64/3.65 3.52/3.52 3.41/3.40 3.30/3.30 3.20/3.21 3.11/3.13 3.02/3.06 2.94/2.99 2.87/2.93 2.79/2.87 2.73/2.81 2.66/2.76 2.60/2.72 2.54/2.67 2.49/2.63 2.44/2.59 2.39/2.55 2.34/2.51 2.30/2.48 2.25/2.44
(c) Erosion Factors — Doweled Joints, Concrete Shoulder (Single Axle/Tandem Axle) 4 4.5 5 5.5
3.28/3.30 3.13/3.19 3.01/3.09 2.90/3.01
3.24/3.20 3.09/3.08 2.97/2.98 2.85/2.89
3.21/3.13 3.06/3.00 2.93/2.89 2.81/2.79
3.19/3.10 3.04/2.96 2.90/2.84 2.79/2.74
3.15/3.09 3.01/2.93 2.87/2.79 2.76/2.68
3.12/3.08 2.98/2.91 2.85/2.77 2.73/2.65
62-58
The Civil Engineering Handbook, Second Edition
TABLE 62.21 (continued)
Erosion Factors for Erosion Analysis
Slab Thickness (in.)
50
100
200
300
500
700
6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14
2.79/2.93 2.70/2.86 2.61/2.79 2.53/2.73 2.46/2.68 2.39/2.62 2.32/2.57 2.26/2.52 2.20/2.47 2.15/2.43 2.10/2.39 2.05/2.35 2.00/2.31 1.95/2.27 1.91/2.23 1.86/2.20 1.82/2.17
2.75/2.82 2.65/2.75 2.56/2.68 2.48/2.62 2.41/2.56 2.34/2.51 2.27/2.46 2.21/2.41 2.15/2.36 2.09/2.32 2.04/2.28 1.99/2.24 1.94/2.20 1.89/2.16 1.85/2.13 1.81/2.09 1.76/2.06
2.70/2.71 2.61/2.63 2.52/2.56 2.44/2.50 2.36/2.44 2.29/2.39 2.22/2.34 2.16/2.29 2.10/2.25 2.04/2.20 1.99/2.16 1.93/2.12 1.88/2.09 1.84/2.05 1.79/2.01 1.75/1.98 1.71/1.95
2.68/2.65 2.58/2.57 2.49/2.50 2.41/2.44 2.33/2.38 2.26/2.32 2.19/2.27 2.13/2.22 2.07/2.18 2.01/2.14 1.95/2.09 1.90/2.05 1.85/2.02 1.81/1.98 1.76/1.95 1.72/1.91 1.67/1.88
2.65/2.58 2.55/2.50 2.46/2.42 2.38/2.36 2.30/2.30 2.22/2.24 2.16/2.19 2.09/2.14 2.03/2.09 1.97/2.05 1.92/2.01 1.87/1.97 1.82/1.93 1.77/1.89 1.72/1.86 1.68/1.83 1.64/1.80
2.62/2.54 2.52/2.45 2.43/2.38 2.35/2.31 2.27/2.24 2.20/2.18 2.13/2.13 2.07/2.08 2.01/2.03 1.95/1.99 1.89/1.95 1.84/1.91 1.79/1.87 1.74/1.84 1.70/1.80 1.65/1.77 1.61/1.74
k of Subgrade–Subbase (pci)
(d) Erosion Factors — Aggregate–Interlock Joints, Concrete Shoulder (Single Axle/Tandem Axle) 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14
3.46/3.49 3.32/3.39 3.20/3.30 3.10/3.22 3.00/3.15 2.91/3.08 2.83/3.02 2.76/2.97 2.69/2.92 2.63/2.88 2.57/2.83 2.51/2.79 2.46/2.75 2.41/2.72 2.36/2.68 2.32/2.65 2.28/2.62 2.24/2.59 2.20/2.56 2.16/2.53 2.13/2.51
3.42/3.39 3.28/3.28 3.16/3.18 3.05/3.10 2.95/3.02 2.86/2.96 2.77/2.90 2.70/2.84 2.63/2.79 2.56/2.74 2.50/2.70 2.44/2.65 2.39/2.61 2.33/2.58 2.28/2.54 2.24/2.51 2.19/2.48 2.15/2.45 2.11/2.42 2.08/2.39 2.04/2.36
3.38/3.32 3.24/3.19 3.12/3.09 3.01/3.00 2.90/2.92 2.81/2.85 2.73/2.78 2.65/2.72 2.57/2.67 2.51/2.62 2.44/2.57 2.38/2.53 2.33/2.49 2.27/2.45 2.22/2.41 2.17/2.38 2.13/2.34 2.09/2.31 2.04/2.28 2.00/2.25 1.97/2.23
3.36/3.29 3.22/3.16 3.10/3.05 2.99/2.95 2.88/2.87 2.79/2.79 2.70/2.72 2.62/2.66 2.55/2.61 2.48/2.55 2.42/2.51 2.36/2.46 2.30/2.42 2.24/2.38 2.19/2.34 2.14/2.31 2.10/2.27 2.05/2.24 2.01/2.21 1.97/2.18 1.93/2.15
3.32/3.26 3.19/3.12 3.07/3.00 2.96/2.90 2.86/2.81 2.76/2.73 2.68/2.66 2.60/2.59 2.52/2.53 2.45/2.48 2.39/2.43 2.33/2.38 2.27/2.34 2.21/2.30 2.16/2.26 2.11/2.22 2.06/2.19 2.02/2.15 1.98/2.12 1.93/2.09 1.89/2.06
3.28/3.24 3.15/3.09 3.04/2.97 2.93/2.86 2.83/2.77 2.74/2.68 2.65/2.61 2.57/2.54 2.50/2.48 2.43/2.43 2.36/2.38 2.30/2.33 2.24/2.28 2.19/2.24 2.14/2.20 2.09/2.16 2.04/2.13 1.99/2.10 1.95/2.06 1.91/2.03 1.87/2.00
Source: Portland Cement Association. 1984. Thickness Design for Concrete Highway and Street Pavements. With permission.
FAA Thickness Design Procedure for Rigid Airport Pavements The FAA thickness design method is based on the Westergaard analysis of an edge-loaded slab on a dense liquid foundation. The design curves in Figs. 62.36–62.42 have been developed with the assumption that the landing gear assembly is either tangent to a longitudinal joint or perpendicular to a transverse joint — whichever produces the largest stress. It is also assumed that 95% of the gross aircraft weight is carried on the main landing gear assembly. The design curves provide slab thickness T for the critical areas defined earlier in this chapter. The thickness of 0.9T for noncritical areas applies to the concrete slab
62-59
Highway and Airport Pavement Design
90 40
80
25
20 18
60
50
40 35
EROSION FACTOR
SINGLE AXLE LOAD, KIPS
30
TANDEM AXLE LOAD, KIPS
70
2.0
2
2.2
10,000,000 8 6
2.4
4
2.6
2
2.8
10,000,000 8 6
3.0
4 3.2 2 3.4 100,000 8 6
3.6 3.8
16 30
4
10
25
20
9
18
8
16
100
1.8
90 40
80 70
30
60
25
50
20 18
40 35
16 30
4.0
2
14
10,000 8 6
12
14 12
50
100,000,000 4 2 10,000,000 6 4
2.0
2
2.2
1,000,000 8 6
2.4
4
2.6 2 2.8 3.0
100,000 8 6
3.2
4
3.4 2
ALLOWABLE LOAD REPETITIONS
100
1.6
110
EROSION FACTOR
50
120
TANDEM AXLE LOAD, KIPS
110
60 8 6 4
SINGLE AXLE LOAD, KIPS
100,000,000
120
ALLOWABLE LOAD REPETITIONS
60
3.6 10,000 8
25
6 4
4
10
WITHOUT CONCRETE SHOULDER
20
WITH CONCRETE SHOULDER 2
2 1000
9
18
8
16
1000
,00
60
pci
,0
00
75
k=50 100
800
200 300 500
CONCRETE FLEXURAL STRENGTH, psi
0l
bs
900
00
,0
45 700
00
,0
30
600
0178 E 500
ANNUAL DEPARTURES 1200 3000 6000 15,000 25,000 14 16 15 16 14 13 15 14 15 13 14 12 13 14 12 13 11 12 13 11 12 12 11 10 10 11 11 10 9 10 9 10 9 8 9 8 9 8 7 8 8 7 7 6 7 7
SLAB THICKNESS, in.
FIGURE 62.35 Allowable repetitions for erosion analysis. (Source: Portland Cement Association. 1984. Thickness Design for Concrete Highway and Street Pavements. With permission.)
NOTE: 1 inch = 2.54 cm 1 psi = 0.0069 MN/m2 1 Ib = 0.454 kg 1 pci = 0.272 MN/m3
FIGURE 62.36 Rigid pavement thickness for single-wheel gear. (Source: Federal Aviation Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C. With permission.)
thickness. As in the case for flexible pavement design, stabilized subbase is required to accommodate aircraft weighing 100,000 lb or more. Design Loading. The same method of selecting a design aircraft and computing design annual departures is followed as for the FAA flexible airport pavement design.
62-60
The Civil Engineering Handbook, Second Edition
0,
0
750
00
0,
10
00
,0
700
75
0
650
,00
50
600
550
DUAL WHEEL GEAR 0579 E
500
ANNUAL DEPARTURES 1200 3000 500015,000 25,000 26 27 22 23 24 26 25 21 22 23 25 24 20 21 22 24 23 19 20 21 22 23 22 18 19 20 21 21 17 18 19 20 20 18 19 16 17 19 17 18 15 16 18 16 17 17 15 14 15 16 16 14 13 15 14 15 13 14 12 13 14 12 13 11 12 13 11 12 12 10 11 10 11 11 10 9 10 10 9 9 8 9 8 9 8 7 8 8 7 7
NOTE: 1 inch = 2.54 cm 1 Ib = 0.454 kg
SLAB THICKNESS ,in
FLEXURAL STRENGTH, psi
15
800
00
0
20 0, 00 0
0 pci k=5 100
200 300 500
850
Ib s
900
1 psi = 0.0069 MN/m2 1 pci = 0.272 MN/m3
FIGURE 62.37 Rigid pavement thickness for dual-wheel gear. (Source: Federal Aviation Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C. With permission.)
Concrete Flexural Strength. The 28-day flexural strength of concrete is determined by ASTM Test Method C78. A 90-day flexural strength may be used. It can be taken to be 10% higher than the 28-day strength, except when high early strength cement or pozzolanic admixtures are used. Foundation Modulus. The subgrade modulus k is determined by the test method specified in AASHTO T222. When a layer of subbase is used, the design k is obtained from Fig. 62.43 for unstabilized subbase and Fig. 62.44 for stabilized subbase. High Traffic Volumes. For airports with design traffic exceeding 25,000 annual departures, the FAA suggests using thicker pavements as follows: 104, 108, 110, and 112% of design thickness for 25,000 annual departures for annual departure levels of 50,000, 100,000, 150,000, and 200,000, respectively. This suggestion is based on a logarithmic relationship between percent thickness and departures. Example 62.21 Determine the thickness of concrete pavement required for the design traffic of Example 62.13. The subgrade k = 100 pci. Since the design aircraft exceeds 100,000 lb in gross weight, use 6 in. stabilized subbase. From Fig. 62.44, effective k = 210 pci. Using concrete with flexural strength of 650 psi, the slab thickness required is 18 in., from Fig. 62.37. FAA Joint Spacing and Reinforcement Design for Rigid Airport Pavements The recommended maximum joint spacings are shown in Table 62.22. Tie bars are used across longitudinal joints. They are deformed bars 5/8 in. (16 mm) in diameter, 30 in. (76 cm) long, and spaced 30 in. (76 cm) on centers. Dowel bars are used at transverse joints to prevent relative vertical displacement of adjacent slab ends. Table 62.23 indicates the dowel dimensions and spacings for various slab thicknesses. The area of steel required for a reinforced concrete pavement is determined by
62-61
Highway and Airport Pavement Design
ANNUAL DEPARTURES 1200 3000 5000 15,000 25,000 27 26 22 23 24 26 25 21 25 23 22 24 20 24 22 21 23
30 0,0 00
19
20
21
22
19
20
21
19
20
18
19
17
18
16
17
15
16
00
0
800
0, 00
17
18
16
17
750
15
16
14
15
00
0 0,
10
700
13
21
19 18
12 11
13 12 12
10
13 12 11 11
10 9
8 8 7 7
14
13 12
10
500
15 14
11
9 DUAL TANDEM GEAR 0478 E
15
13
11
600
17 16
14 14
650
550
22
20
15
FLEXURAL STRENGTH , psi
0
20
0,
18
23
SLAB THICKNESS, in.
ci
40 0,0 00 I
k=50 p
100
200
500
300
850
bs
900
10 9 9 8
10 9
8 7
8
NOTE: 1 inch
= 2.54 cm
1 psi = 0.0069 MN/m2
1 Ib
= 0.454 kg
1 pci = 0.272 MN/m3
FIGURE 62.38 Rigid pavement thickness for dual-tandem gear. (Source: Federal Aviation Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C. With permission.)
3.7 ( L ) ( Lt ) 0.5 A s = -----------------------------fs where
(62.36)
As = area of steel per foot width or length, in square inches L = length or width of slab, in feet t = thickness of slab, in inches fs = allowable tensile stress in steel, in psi, taken as two-thirds of the yield strength of the steel
The minimum percentage of steel reinforcement is 0.05%. The maximum allowable slab length regardless of steel percentage is 75 ft (23 m). Example 62.22 An 18-in.-thick concrete airport pavement has a slab length of 50 ft. Determine the longitudinal steel requirement. Using grade 60 steel, fs = 2-- (60,000) = 40,000 psi. By Eq. (62.36), As = 3.7(50) ( 50 ) ( 18 ) /40,000 = 3 0.14 in.2 per ft. This is equal to 0.016% steel, satisfying the minimum requirement of 0.05%.
62.7 Pavement Overlay Design As a pavement reaches the end of its service life, a new span of service life can be provided by either a reconstruction or an application of overlay over the existing pavement. There are three common forms of overlay construction — bituminous overlay on flexible pavement, bituminous overlay on concrete pavement, and concrete overlay on concrete pavement. The Asphalt Institute method of flexible overlay design for highway pavement, the Portland Cement Association method of concrete overlay design for highway pavement, and the Federal Aviation Administration method of overlay design for airport pavement are described in this section.
62-62
The Civil Engineering Handbook, Second Edition
0
0 00 0,
30
0
00
0,
700
650
600
B747-100, SR,200 B,C,F CONTACT AREA = 245 sq. in. DUAL SPACING = 44 in. TANDEM SPACING = 53 in.
550
0378 E
500
ANNUAL DEPARTURES 1200 3000 6000 15,000 25,000 26 22 23 24 25 26 21 22 23 24 25 20 21 22 24 23 19 20 21 22 23 18 19 20 21 22 21 17 18 19 20 20 18 19 16 17 19 17 18 15 16 18 16 17 17 14 15 15 16 16 14 13 15 14 15 13 12 14 13 14 12 13 11 12 13 11 12 10 12 11 10 11 11 10 9 10 9 10 9 8 9 8 9 8 7 8 8 7 7
SLAB THICKNESS, in.
00 0, 00
750
40
FLEXURAL STRENGTH , psi
50
800
60
0 ,0
ci k=50 p
100
200 300 500
850
85 0 80 ,000 0,0 Ib 00 s 70 0,0 00
900
NOTE: 1 inch = 2.54 cm 1 psi = 0.0069 MN/m2 1 Ib = 0.454 kg 1 pci = 0.272 MN/m3
FIGURE 62.39 Rigid pavement thickness for B-747-100, SR, 200B, 200C, and 200F. (Source: Federal Aviation Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C. With permission.)
AI Design Procedure for Flexible Overlay on Flexible Highway Pavement The Asphalt Institute [1983] presents two different approaches to flexible overlay design — one based on the concept of effective thickness and the other based on deflection analysis. AI Effective Thickness Approach This approach evaluates the so-called effective thickness Te of the existing pavement and determines the required overlay thickness TOL as T OL = T – T e
(62.37)
where T is the required thickness of a new full-depth pavement if constructed on the existing subgrade, to be determined from Fig. 62.10. The Asphalt Institute recommends two methods for evaluating effective pavement thickness. The first method involves the use of a conversion factor C based on the PSI (present serviceability index) of the existing pavement plus the use of conversion factors E for converting various pavement layers into equivalent thickness of asphalt concrete. That is, n
Te = C Â { h i E i }
(62.38)
i=1
where n is the total number of pavement layers. C is obtained from either line A or line B in Fig. 62.45. Line A assumes that the overlaid pavement would exhibit a reduced rate of change in PSI compared to before overlay. Line B represents a more conservative design, assuming that the rate of change in PSI
62-63
Highway and Airport Pavement Design
ANNUAL DEPARTURES 1200 3000 6000 15,000 25,000
22
lb s 00 0,0 0,0
00
70
24
22
23
20
21
22
23
19
20
21
22
18
19
20
21
17
18
19
20
16
17
18
19
16
17
18
15
17
15
16
14
15
16
13
14
21
25 24
50
FLEXURAL STRENGTH , psi
0,
00
0
60
pci k=50
200
500
300
800
100
850
26 23
750
0 00
,
0 40 700
0
0 ,0
0
30 650
12 11 B 747 SP CONTACT AREA = 210 sq. in. DUAL SPACING = 43.25 in. TANDEM SPACING = 54 in.
600
550
10 9
13
0278 E
12 11 11
500
23 22 21 20
16 15 14 13 12
10 9 9 8 7
18
15
10
7
24
17
11
10
8 7
14
12
8
25
19
13
9
26
8
SLAB THICKNESS, in.
900
14 13 12 11 10 9 8
NOTE: 1 inch = 2.54 cm 1 psi = 0.0069 MN/m2 1 Ib = 0.454 kg 1 pci = 0.272 MN/m3
FIGURE 62.40 Rigid pavement thickness for B-747-SP. (Source: Federal Aviation Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C. With permission.)
would remain unchanged after overlay. PSI is usually estimated from correlation with pavement roughness measurements. Equivalency factors Ei are obtained from Table 62.24. Example 62.23 An old pavement has 3-in. asphalt surface course and 8.5-in. type II emulsified asphalt base (see Example 62.12). Its current PSI is 2.8. Provide an overlay to the pavement to carry the design traffic of Example 62.10. With PSI = 2.8, C = 0.75 by line A of Fig. 62.45. The thickness of new full-depth asphalt pavement required is 9.5 in. (see Example 62.12). The equivalency factor of type II emulsified base is 0.83, from Table 62.24. Overlay thickness Te = 9.5 – 0.75{(3 ¥ 1.0) + (8.5 ¥ 0.83)} = 2 in. The second recommended method relies on component analysis that assigns conversion factors Ci from Table 62.25 to individual pavement layers based on their respective physical conditions. The effective thickness for the existing pavement structure is given by n
Te = where
ÂhiCi i=1
(62.39)
hi = the layer thickness of layer i n = the total number of layers in the existing pavement
Example 62.24 For the old pavement in Example 62.23, it is observed that the asphalt concrete surface exhibits appreciable cracking and the emulsified asphalt base has some fine cracking and slight deformation in the wheel paths. Design an overlay for the same traffic as in Example 62.23.
62-64
The Civil Engineering Handbook, Second Edition
ANNUAL DEPARTURES 1200 3000 6000 15,000 25,000
23
20
21
22
19
20
21
18
19
20
17
18
19
17
18
16
17
15
16
0,0
30 0, 00
FLEXURAL STRENGTH , psi
15
16 15
20
14 14 13
650
13 12 12 DC 10-10, 10 CF
600
14 13
11
CONTACT AREA = 294 sq. in. DUAL SPACING = 54 in. TANDEM SPACING = 64 in.
10 9
550 8 0278 E 7
11 10
8
22 21 20
17 16 15
14 13 12 11 10
9 9 8
18
15
10 9
23
19
12
11
24
SLAB THICKNESS ,in
21
22
00
23
16 00
25
22
17
0 0,
24
21
18
700
25
24
19
750
27 26
23
20
800
26 22
40
pci k=50
100
200 300 500
850
45 0,0 00
Ibs .
900
14 13 12 11 10 9
8
8 7 NOTE: 1 inch = 2.54 cm 1 psi = 0.0069 MN/m2 1 Ib = 0.454 kg 1 pci = 0.272 MN/m3
500
7
FIGURE 62.41 Rigid pavement thickness for DC 10-10, 10CF. (Source: Federal Aviation Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C. With permission.)
From Table 62.25, the conversion factors for the surface and base courses are both 0.6. TOL = 9.5 – {(0.6 ¥ 3) + (0.6 ¥ 8.5)} = 2.6 in. Use 3 in. AI Deflection-Based Approach This approach is based on the correlation between wheel load, repetitions of wheel loads, and the magnitude of pavement rebound deflection. Rebound deflections are measured using the Benkelman beam on the outer wheel path at a minimum of 10 locations within the test section or a minimum of 20 measurements per mile (12 per km). The Benkelman beam is a 12-ft (3.66-m) beam pivoted at a point 8 ft (2.44 m) from the probe end. The probe is positioned at the test point between the dual tires of a rear wheel of a loaded truck that has an 18-kip (80-kN) load equally distributed on its two dual wheels of the rear axle. The amount of vertical rebound at the test point after the truck moves away is recorded as the rebound deflection. The deflection measurements are used to determine a representative rebound deflection d r:
d r = ( d m – 2s ) Fc where
(62.40)
d m = the mean of rebound deflection measurements s = the standard deviation F = the temperature adjustment factor c = the critical period adjustment factor
The factor c converts the measured deflection to the maximum deflection that would have occurred if the test were performed at the most critical time of the year. Numerically, it is equal to the ratio of measured deflection to the corresponding deflection measurement if it were to be made during the critical
62-65
Highway and Airport Pavement Design
ANNUAL DEPARTURES 1200 3000 6000 15,000 25,000
Ib s 60 0, 00 0
21
00
0
40
700 0
0 0,0
20
650
550
CONTACT AREA = 331 sq. in. DUAL SPACING = 54 in. TANDEM SPACING = 64 in. CENTER GEAR SPACING = 37.5 in.
500
24
22 21
22
23
19
20
21
22
18
19
20
21
17
18
19
20
16
17
18
19
15
16
17
18
16
17
15
16
14
15
13
14
14
15
13
14
10
13
12 11 11 10
9
7
13 12
10
23 22 21
18 17 16 15 14 13 12 11
10
10
9
9
8
8
9 7
24
19
11
9 8
25
20
12
8 0478 E
26
20
12
DC-10-30, 30 CF, -40, 40 CF
27
25
24 23
11 600
26 23
0,
750
30
FLEXURAL STRENGTH , psi
800
0, 00
0
50 0, 00 0
pci k=50
100 200 300 500
850
22
8 7
SLAB THICKNESS, in.
900
NOTE: 1 inch = 2.54 cm 1 psi = 0.00069 MN/m2 1 Ib =0.454 kg 1 pci = 0.272 MN/m3
FIGURE 62.42 Rigid 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.)
period. It can be established from historical records or derived from engineering judgment when no record is available. F is determined from Fig. 62.46 with two inputs: thickness of untreated granular base and mean pavement temperature. The estimation of mean pavement temperature requires information of the pavement surface temperature at the time of test and the 5-day mean air temperature computed from the maximum and minimum air temperature for each of the 5 days prior to the date of deflection testing. Fig. 62.47 is used to obtain temperature at the middepth and bottom of the pavement. Next, the surface temperature, middepth temperature, and bottom temperature are averaged to provide the mean pavement temperature. Having computed the representative rebound deflection, Fig. 62.48 is used to determine the required overlay thickness. The design ESAL is estimated by means of the procedure described under the heading of traffic-loading computation. Example 62.25 Rebound deflection measurements made at 12 randomly selected locations on an old asphalt pavement using Benkelman beam produced the following net rebound deflections in in.: 0.038, 0.035, 0.039, 0.039, 0.039, 0.039, 0.044, 0.044, 0.037, and 0.036. The temperature of pavement surface was found to be 131˚F. The extreme air temperatures in the previous 5 days were (88˚F, 75˚F), (86˚F, 75˚F), (90˚F, 77˚F), (88˚F, 77˚F), and (88˚F, 75˚F). The thickness of the asphalt layer was 6 in. The thickness of untreated granular base was 12 in. Determine the overlay thickness required to carry additional ESAL of 5 ¥ 106. Mean deflection d m = 0.0391 in. and standard deviation s = 0.0029. Five-day mean air temperature = 81.9˚F. From Fig. 62.47, pavement layer middepth temperature T1 = 105˚F and bottom temperature T2 = 100˚F. Mean pavement temperature = 112˚F. From Fig. 62.46, F = 0.82. Assuming a critical period factor of c = 0.9, dr = {0.0391 + 2(0.0029)} ¥ (0.82)(0.9) = 0.0331 in. For design ESAL of 5 ¥ 106, read from Fig. 62.48, the overlay thickness is 3 in.
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The Civil Engineering Handbook, Second Edition
( cm ) 12
14
16
18
20
24
22
26
28
30
32
34
500
125 K = 300 (81) K = 200 (54)
LB / IN3
300 200
K = 100
100 75
(27)
50 40
100
K = 50 GRADE
30
(14)
EFFECTIVE K ON TOP OF SUBBASE
SUB
50
( MN /m3 )
400
20 15
4
5
6
7 8 9 10 11 THICKNESS OF SUBBASE, INCHES
12
13
14
WELL - GRADED CRUSHED AGGREGATE
( cm ) 12
14
16
18
20
22
24
26
28
30
32
34
500
125 K = 300 (81) 4) K = 200 (5
LB / IN3
300 200
K = 100
100 75 50
(27)
40 30
100
4)
(1 K = 50 GRADE
SUB
50
( MN / m3 )
400
20 15
4
5
6
7 8 9 10 11 THICKNESS OF SUBBASE, INCHES
12
13
14
BANK - RUN SAND & GRAVEL (P1 < 6)
FIGURE 62.43 Effect of subbase on subgrade modulus. (Source: Federal Aviation Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C, p. 25. With permission.)
AI Design Procedure for Flexible Overlay on Rigid Highway Pavement Two design procedures are presented by the Asphalt Institute [1983], namely, the effective thickness procedure and the deflection procedure. AI Effective Thickness Procedure The component analysis procedure described earlier for asphalt overlay on flexible pavement also applies for the design of asphalt overlay on concrete pavement. The same table (Table 62.25) is used for both.
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Highway and Airport Pavement Design
12
14
16
( CM ) 20 22
18
24
26
28
30
500
1) K = 300 (8 0 (54) 0 2 = K
300 K=
100
120 100 90 80
(27)
70 60
200 50
)
DE
K
0 =5
(14
40 35
A GR
( MN / m3 )
K ON TOP OF SUBBASE LB / IN3
400
B
SU
30
100 90 80
25 20
70 60
15 50
4
5 6 7 8 9 10 11 THICKNESS OF SUBBASE, INCHES
12
FIGURE 62.44 Effect of stabilized subbase on subgrade modulus. (Source: Federal Aviation Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C, p. 64. With permission.) TABLE 62.22
FAA Recommended Maximum Joint Spacings
Slab Thickness 12 in. (31 cm)
Transverse Spacing
Longitudinal Spacing
15 ft (4.6 m) 20 ft (6.1 m) 25 ft (7.6 m)
12.5 ft (3.8 m) 20 ft (6.1 m) 25 ft (7.6 m)
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.
TABLE 62.23
Dowel Bar Dimensions and Spacings
Slab Thickness 6–7 in. (15–18 cm) 8–12 in. (21–31 cm) 13–16 in. (33–41 cm) 17–20 in. (43–51 cm) 21–24 in. (54–61 cm)
Diameter
Length
Spacing
0.75 in. (20 mm) 1 in. (25 mm) 1.25 in. (30 mm)* 1.50 in. (40 mm)* 2 in. (50 mm)*
18 in. (46 cm) 19 in. (48 cm) 20 in. (51 cm) 20 in. (51 cm) 24 in. (61 cm)
12 in. (31 cm) 12 in. (31 cm) 15 in. (38 cm) 18 in. (46 cm) 18 in. (46 cm)
* Dowels may be a solid bar or high-strength pipe. High-strength pipe dowels must be plugged on each end with a tight-fitting plastic cap or with bituminous or mortar mix. 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.
AI Deflection-Based Procedure Deflection measurements are made using Benkelman beam or other devices at the following locations: (a) the outside edge on both sides of two-lane highways; (b) the outermost edge of divided highways; and (c) corners, joints, cracks, and deteriorated pavement areas.
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CONVERSION FACTOR
The Civil Engineering Handbook, Second Edition
0.9 LINE
0.8
LINE
0.7
A
B
0.6 0.5 3.5
3.0 2.5 PRESENT SERVICEABILITY INDEX (PSI)
2.0
1.5
FIGURE 62.45 PSI-based conversion factors for determining effective thickness. (Source: Asphalt Institute. 1983a. Asphalt Overlays for Highway and Street Rehabilitation. Manual Series MS-17, p. 51. With permission.) TABLE 62.24 Asphalt Institute Equivalency Factors for Converting Layers of Other Material Types to Equivalent Thickness of Asphalt Concrete Material Type Asphalt concrete Type I emulsified asphalt base Type II emulsified asphalt base Type III emulsified asphalt base
Equivalency Factor Ei 1.00 0.95 0.83 0.57
Source: Asphalt Institute. 1983. Asphalt Overlays for Highway and Street Rehabilitation. MS-17. p. 52. With permission.
For JPCP and JRCP the differential vertical deflection at joints should be less than 0.05 mm (0.002 in.) and the mean deflection should be less than 0.36 mm (0.014 in.). For CRCP, Dynaflect deflections of 15 to 23 mm (0.0006 to 0.0009 in.) or greater lead to excessive cracking and deterioration. Undersealing or stabilization is required when the deflection exceeds 15 mm (0.0006 in.). Dense-graded asphalt concrete overlay can reduce deflections by 0.2% per mm (5% per in.) of thickness. However, depending on the mix type and environmental conditions, deflection may be as high as 0.4 to 0.5% per mm (10 to 12% per in.). If a reduction of 50% or more of deflection reduction is required, it is more economical to apply undersealing before overlay is considered. For a given slab length and mean annual temperature differential, the required overlay thickness is selected from Fig. 62.49. The thicknesses are provided to minimize reflective cracking by taking into account the effects of horizontal tensile strains and vertical shear stresses. The design chart has three sections — A, B, and C. In section A, a minimum thickness of 100 mm (4 in.) is recommended. This thickness should reduce the deflection by an estimated 20%. In sections B and C, the thicknesses may be reduced if the pavement slabs are shortened by breaking and seating (denoted as alternative 2 in Fig. 62.49) to reduce temperature effects. This is recommended as an overlay thickness approaches the 200- to 225-mm (8- to 9-in.) range. Another alternative is the use of a crack relief layer (denoted as alternative 3 in Fig. 62.49). A recommended crack relief structure is a 3.5-in.thick layer of coarse, open-graded hot mix containing 25 to 35% interconnecting voids and made up of 100% crushed material. It is overlain by a dense-graded asphalt concrete surface course (at least 1.5 in. thick) and a dense-graded asphalt concrete leveling course (at least 2 in. thick). Example 62.26 The vertical deflections measured by a Benkelman beam test at a joint of a portland cement concrete pavement are 0.042 and 0.031 in. The pavement has a slab length of 40 ft. Design an asphalt concrete overlay on the concrete pavement. The design temperature differential is 80˚F.
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Highway and Airport Pavement Design
TABLE 62.25 Case I
II III IV
V
VI
VII
Conversion Factors C for Determining Effective Thickness Description
(a) Native subgrade in all cases. (b) Improved subgrade, predominantly granular material, may contain some silt and clay but have P.I. of 10 or less. (c) Lime-modified subgrade constructed from high-plasticity soils, P.I. greater than 10. Granular subbase or base, reasonably well-graded, hard aggregates with some plastic fines and CBR not less than 20. Use upper part of range if P.I. is 6 or less, lower part of range if P.I. is more than 6. Cement or lime–fly ash stabilized subbases and bases constructed from low-plasticity soils, P.I. of 10 or less. (a) Emulsified or cutback asphalt surfaces and bases that show extensive cracking, considerable raveling or aggregate degradation, appreciable deformation in the wheel paths, and lack of stability. (b) Portland cement concrete pavements (including those under asphalt surfaces) that have been broken into small pieces 2 ft (0.6 m) or less in maximum dimension prior to overlay construction. Use upper part of range when subbase is present, lower part of range when slab is on subgrade. (c) Cement or lime–fly ash stabilized bases that have developed pattern cracking, as shown by reflected surface cracks. Use upper part of range when cracks are narrow and tight, lower part of range with wide cracks, pumping, or evidence of instability. (a) Asphalt concrete surface and base that exhibit appreciable cracking and crack patterns. (b) Emulsified or cutback asphalt surface and bases that exhibit some fine cracking, some raveling or aggregate degradation, and slight deformation in the wheel paths but remain stable. (c) Appreciably cracked and faulted portland cement concrete pavement (including such under asphalt surfaces) that cannot be effectively undersealed. Slab fragments, ranging in size from approximately 10 to 160 ft2 (1 to 4 m2), have been well seated on the subgrade by heavy pneumatic-tired rolling. (a) Asphalt concrete surfaces and bases that exhibit some fine cracking, have small intermittent cracking patterns and slight deformation in the wheel paths but remain stable. (b) Emulsified or cutback asphalt surface and bases that are stable, generally uncracked, show no bleeding, and exhibit little deformation in the wheel paths. (c) Portland cement concrete pavements (including such under asphalt surfaces) that are stable and undersealed, have some cracking but contain no pieces smaller than about 10 ft2 (1 m2). (a) Asphalt concrete, including asphalt concrete base, generally uncracked, and with little deformation in the wheel paths. (b) Portland cement concrete pavement that is stable, undersealed, and generally uncracked. (c) Portland cement concrete base, under asphalt surface, that is stable, nonpumping, and exhibits little reflected surface cracking.
Factor C 0.0
0.1–0.2 0.2–0.3 0.3–0.5
0.5–0.7
0.7–0.9
0.9–1.0
Source: Asphalt Institute. 1983a. Asphalt Overlays for Highway and Street Rehabilitation. Manual Series MS-17, pp. 54–55. With permission.
Mean vertical deflection is 0.0365 in., and the differential deflection is 0.009 in. Alternative 1. Thick overlay: From Fig. 62.49, more than 9 in. of overlay is required. Use either alternative 2 or 3. Alternative 2. Break and seat to reduce slab length: Break slab into 20-ft sections. From Fig. 62.49, 5.5 in. of overlay is required. For the overlaid pavement, mean vertical deflection = 0.0365 – {(5.5 ¥ 5%) ¥ 0.0365} = 0.0265 > 0.014 in., and vertical differential deflection = 0.009 – {(5.5 ¥ 5%) ¥ 0.009} = 0.0025 > 0.002 in. Undersealing is needed. Alternative 3. Crack relief layer: Use 3.5-in. crack relief course with 1.5-in. surface course and 2-in. leveling course, giving a total of 7-in. asphalt concrete courses. Similar procedure of deflection checks to those for alternative 2 indicates that undersealing is required.
PCA Design Procedure for Concrete Overlay on Concrete Highway Pavement Depending on the bonding between the overlay and the existing pavement slab, concrete overlays can be classified into three types: bonded, unbonded, and partially bonded. Bonded overlay is achieved by applying a thin coating of cement grout before overlay placement. The construction of unbonded overlay involves the use of an unbonding medium at the surface of the existing pavement. Asphaltic concrete and sand asphalt are common unbonding media. Partially bonded overlay refers to a construction in
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The Civil Engineering Handbook, Second Edition
UNTREATED GRANULAR BASE THICKNESS 0¢¢ 3¢¢ 25¢¢ 120
MEAN PAVEMENT TEMPERATURE
110
DEFLECTION ADJUSTMENT FACTORS FOR BENKELMAN BEAM TESTING
100 90 80 70 60 50 25¢¢ 40
0¢¢
19¢¢ 12¢¢
30 0.0
0.2
0.4
3¢¢
6¢¢
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 TEMPERATURE ADJUSTMENT FACTOR (F)
2.2
2.4
FIGURE 62.46 Chart for determining temperature correction factor F. (Source: Asphalt Institute. 1983a. Asphalt Overlays for Highway and Street Rehabilitation. Manual Series MS-17. With permission.) PAVEMENT SURFACE TEMPERATURE PLUS 5-DAY MEAN AIR TEMPERATURE, ∞F 0
20
40
60
80
100
120
140
160
180
200
220
70
140
60
DEPTH IN PAVEMENT 25mm (1 in.)
50
120
50mm (2 in.)
40
100mm (4 in.)
100 300mm 200mm (12 in.) 150mm (8 in.) (6 in.)
30 20
80 60
10 40 0
TEMPERATURE AT DEPTH, ∞F
TEMPERATURE AT DEPTH, ∞C
240 260 160
20
-10 -10
0
10
20
30
40
50
60
70
80
90
100
110 120
PAVEMENT SURFACE TEMPERATURE PLUS 5-DAY MEAN AIR TEMPERATURE, ∞C
FIGURE 62.47 Estimation of pavement temperature. (Source: Asphalt Institute. 1983a. Asphalt Overlays for Highway and Street Rehabilitation. Manual Series MS-17. With permission.)
which the overlay is placed directly on the existing pavement without the application of a bonding or unbonding medium. Design of Unbonded Overlay The procedure selects an overlay thickness that, under the action of an 18-kip (80-kN) single-axle load, would have an edge stress in the overlay equal to or less than the corresponding edge stress in an adequately
62-71
Highway and Airport Pavement Design
16
Overlay Thickness (in.)
14
ESAL 10,000,000
20,000,000
50,000,000
5,000,000
12
10
2,000,000
8
1,000,000 500,000
6 200,000 100,000 50,000 20,000 10,000 5,000
4
2 0 0
2
4
6
8
10
12
14
16
18
Representative Rebound Deflection (0.01 in.)
FIGURE 62.48 Design chart for overlay thickness. (Source: Asphalt Institute. 1983a. Asphalt Overlays for Highway and Street Rehabilitation. Manual Series MS-17. With permission.)
designed new pavement under the same load. Design charts in Fig. 62.50 are provided for the following three cases: Case 1. Existing pavement exhibiting a large amount of midslab and corner cracking; poor load transfer at cracks and joints. Case 2. Existing pavement exhibiting a small amount of midslab and corner cracking; reasonably good load transfer across cracks and joints; localized repair performed to correct distressed slabs. Case 3. Existing pavement exhibiting a small amount of midslab cracking; good load transfer across cracks and joints; loss of support corrected by undersealing. The design charts were obtained from computer analysis of pavements assuming modulus of elasticity of 5 ¥ 106 psi (35 GPa) for overlays and 3 ¥ 106 and 4 ¥ 106 psi (21 and 28 GPa) for existing pavements. If a tied shoulder is provided, the thickness of the overlay may be reduced by 1 in. (25 mm) subject to the minimum thickness requirement of 6 in. (150 mm). Example 62.27 Design a concrete overlay for an existing 10-in.-thick concrete pavement if the required new single-slab thickness is 10 in. For case 1, TOL = 9 in., from Fig. 62.50(a). For case 2, TOL = 6 in., from Fig. 62.50(b). For case 3, where TOL < 6 in., from Fig. 62.50(c), use minimum 6 in. Design of Bonded Overlay The same structural equivalency concept as for unbonded overlay is adopted in the design for bonded overlay, except that the comparison is now made between the stress-to-strength ratios of the new and the overlaid pavements. The design chart (Fig. 62.51) has three curves for three different ranges of moduli of rupture Sc of the existing concrete. Sc may be estimated from the effective splitting tensile strength fte as follows:
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The Civil Engineering Handbook, Second Edition
TEMPERATURE DIFFERENTIAL ∑ (∞F) Slab Length (Ft)
30
10 or Less
100mm (4 in.)
100mm (4 in.)
100mm (4 in.)
100mm (4 in.)
100mm (4 in.)
100mm (4 in.)
3
15
100mm (4 in.)
100mm (4 in.)
100mm (4 in.)
100mm (4 in.)
100mm (4 in.)
100mm (4 in.)
4.5
20
100mm (4 in.)
100mm (4 in.)
100mm (4 in.)
100mm (4 in.)
125mm (5 in.)
140mm (5.5 in.)
6
25
100mm (4 in.)
100mm (4 in.)
100mm (4 in.)
125mm (5 in.)
150mm (6 in.)
30
100mm (4 in.)
100mm (4 in.)
35
100mm (4 in.)
40
100mm (4 in.)
45
115mm (4.5 in.)
50
40
125mm (5 in.)
60
150mm (6 in.)
150mm (6 in.)
175mm (7 in.)
140mm (5.5 in.)
175mm (7 in.)
200mm (8 in.)
150mm (6 in.)
190mm (7.5 in.)
225mm (9 in.)
115mm (4.5 in.)
70
175mm (7 in.)
80
175mm (7 in.) 200mm (8 in.)
Slab Length (m)
7.5 9
Use Alternative 2 or 3
10.5
Use Alternative 2 or 3
Use Alternative 2 or 3
12
Use Alternative 2 or 3
Use Alternative 2 or 3
13.5
215mm (8.5 in.)
50
125mm (5 in.)
175mm (7 in.)
215mm (8.5 in.)
Use Alternative 2 or 3
Use Alternative 2 or 3
Use Alternative 2 or 3
15
60
150mm (6 in.)
200mm (8 in.)
Use Alternative 2 or 3
Use Alternative 2 or 3
Use Alternative 2 or 3
Use Alternative 2 or 3
18
28
33
39
44
17
22
TEMPERATURE DIFFERENTIAL (∞C)
FIGURE 62.49 Thickness of asphalt overlay on concrete pavement. (Source: Asphalt Institute. 1983a. Asphalt Overlays for Highway and Street Rehabilitation. Manual Series MS-17, p. 79. With permission.)
fte = f t – 1.65s
(62.41)
S c = 0.9A fte
(62.42)
where ft is the average value of splitting tensile strength of cored specimens determined according to ASTM Test Method C496, s is the standard deviation of splitting tensile strength, and A is a regression constant ranging from 1.35 to 1.55. An A value of 1.45 is suggested in the absence of local information. One core should be taken every 300 to 500 ft (91 to 152 m) at midslab and about 2 ft (0.6 m) from the edge of the outside lane. The 0.9 factor in Eq. (62.42) relates the strength of the concrete specimens to that near or at the edge. Example 62.28 A 9-in.-thick concrete pavement is to be strengthened to match the capacity of a new 10-in.-thick concrete pavement. What is the required thickness of bonded overlay if the existing concrete has a flexural strength of 450 psi? Using curve 3 of Fig. 62.51, the thickness of existing pavement plus overlay = 11.5 in. Overlay thickness = 11.5 – 9 = 2.5 in.
FAA Design Procedure for Flexible Overlay on Flexible Airport Pavement The design method of FAA [1978] is similar in the equivalent thickness concept to the PCA method that adopts the component analysis. The FAA equivalency factors are shown in Table 62.13. A high-quality material may be converted to a lower-quality material — for example, surfacing to base and base to
62-73
Highway and Airport Pavement Design
Existing Pavement Thickness (in.) 4
5
6
7
8
9
10
Overlay Existing
Case 1
Overlay Thickness (in.) 6
k = 100—300 pci
7 Base Line
8
8 9 10 11 12 9 10 11 12 13 New Full-Depth Slab Thickness (in.)
14
( a ) Case 1
Existing Pavement Thickness (in.) 4
5
6
7
8
9
10
Overlay Existing
Case 2
k = 100—300 pci Overlay Thickness (in.) 6
Base Line
8
7 8 9 10 11 12 9 10 11 12 13 New Full-Depth Slab Thickness (in.)
14
( b ) Case 2
Existing Pavement Thickness (in.) 4
5
6
8
8
9
10
Overlay Existing
Case 3
Base Line
7
Overlay Thickness (in.) 6 7 8 9 10 11
k = 100—300 pci
9 10 11 13 12 New Full-Depth Slab Thickness (in.) (c) Case 3
14
FIGURE 62.50 PCA design charts for unbonded overlays. (Source: Tayabji, S.D. and Okamoto, P.A., Proceedings 3rd Int. Conf. on Concrete Pavement Design and Rehabilitation, Purdue University, April 23–25, 1985, pp. 367–379. With permission.)
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The Civil Engineering Handbook, Second Edition
Total Thickness of Existing Pavement and Resurfacing. in. 9 10 11 12 13
8
14
Resurfacing Existing Pavement
1
2
Existing Pavement Flexural Strength, psi
1 2 3
526 to 575 476 to 525 426 to 475
3
Base Line
8
Curve No.
9
10 11 12 Full Depth Stab Thickness, In
13
14
FIGURE 62.51 PCA design charts for bonded overlays. (Source: Tayabji, S.D. and Okamoto, P.A., Proceedings 3rd Int. Conf. on Concrete Pavement Design and Rehabilitation, Purdue University, April 23–25, 1985, pp. 367–379. With permission.)
subbase. A material may not be converted to a higher-quality material. The overlay thickness is equal to the difference between the total equivalent layer thicknesses of the existing pavement and the corresponding required layer thickness of a new pavement. The minimum overlay thickness allowed is 3 in. (75 mm). Example 62.29 An existing asphalt concrete airport pavement has 4-in. bituminous surface course, 7-in. base course, and 14-in. subbase. The CBR of the subgrade is 8 and that of the subbase is 12. Provide an overlay to strengthen the pavement for 6000 annual departures of a design aircraft (dual-wheel landing gear) with maximum weight of 100,000 lb. From Fig. 62.17, a new pavement requires 30 in. total thickness based on subgrade CBR of 8 and a thickness of 17 in. above subbase, based on subbase CBR of 12. Using 4 in. of asphalt concrete surface course, the base layer is (17 – 4) = 13 in. The deficiency of thickness of the existing pavement is all in the base layer. Assuming that the existing asphalt concrete surface course can be converted to base at an equivalency ratio of 1.4 to 1 (see Table 62.13), the thickness of asphalt base required = (13 – 7)/1.4 = 4.3 in. An additional 0.3 in. of asphalt concrete base is needed. The total thickness of overlay = (4 in. of new surface course) + 0.3 = 4.3 in. Use a 4.5-in. overlay.
FAA Design Procedure for Flexible Overlay on Concrete Airport Pavement The equation for computing bituminous overlay thickness T is T ( inches ) = 2.5 ( F h – C b h e ) where
(62.43)
F = factor to be obtained from Fig. 62.52 h = single thickness of rigid pavement required for design condition, in inches (use the exact value without rounding off )
62-75
Highway and Airport Pavement Design
MODULUS OF SUBGRADE REACTION pci 1.0
0
100
200
300 0 00 0 25 500 1 00 60
30
0.9
400
00
12
AL NU AN
ES UR RT PA DE
F - FACTOR
00
0.8
0.7
0.6 [0]
[25]
[50]
[75]
[100]
MN/m3
FIGURE 62.52 Graph for determination of F factor. (Source: Federal Aviation Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C, p. 105. With permission.)
Cb = condition factor for base pavement, 0.75 £ Cb £ 1.0 he = thickness of existing rigid pavement, in inches The F factor is related to the degree of cracking that will occur in the base pavement. It has a value less than one, indicating that the entire single concrete slab thickness is not needed because a bituminous overlay pavement is allowed to crack and deflect more than a conventional rigid pavement. Cb is an assessment of the structural integrity of the existing pavement. Cb is 1.0 when the existing slabs contain nominal initial cracking and 0.75 when the slabs contain multiple cracking. Example 62.30 An existing 10-in. concrete pavement has a condition factor Cb of 0.8. The subgrade k is 200 pci. Provide a bituminous overlay to strengthen the pavement to be equivalent to a single rigid pavement thickness of 12 in. for a design traffic of 3000 annual departures. From Fig. 62.52, F = 0.92. By Eq. (62.43), overlay thickness t = 2.5{(0.92 ¥ 12) – (0.8 ¥ 10)} = 7.6 in. Use an 8-in.-thick overlay.
FAA Design Procedure for Concrete Overlay on Concrete Airport Pavement The design of concrete overlay requires an assessment of the structural integrity of the existing pavement and the thickness of a new concrete pavement on the existing subgrade. The design equations are Unbonded overlay Partially bonded overlay Bonded overlay where
T = ( h 2 – Cr h e2 ) 1 § 2
(62.44)
T = ( h 1.4 – C r h e1.4 ) 1 § 1.4
(62.45)
T = h – he
(62.46)
Cr = 1.0 for existing pavement in good condition — some minor cracking evident but no structural defects Cr = 0.75 for existing pavement containing initial corner cracks due to loading but no progressive cracking or joint faulting Cr = 0.35 for existing pavement in poor structural condition — badly cracked or crushed and faulted joints.
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The variables h and he are the thicknesses of new and existing pavements, respectively. The use of partially bonded overlay — which is constructed directly on an existing pavement without debonding medium (such as a bituminous leveling course) — is not recommended for an existing pavement with Cr less than 0.75. Bonded overlays should be used only when the existing rigid pavement is in good condition. The minimum bonded overlay thickness is 3 in. For partially and unbonded overlays, the minimum thickness is 5 in. Example 62.31 An existing 10-in.-thick concrete airport pavement with Cr = 1.0 is to be strengthened to match the capacity of a new 12-in. rigid pavement. Determine the required thickness of bonded, partially bonded, and unbonded overlays. Unbonded overlay. T = 12 2 – 10 2 = 6.6 in. Use 7 in. Partially bonded overlay. T = 1.4 12 1.4 – 10 1.4 = 4.1 in. Use 5 in. (min). Bonded overlay. T = 12 – 10 = 2 in. Use 3 in. (min).
Defining Terms Asphalt pavement (asphalt concrete pavement, bituminous pavement) — The most common form of flexible pavement in which the surface course is constructed of asphaltic (or bituminous) mixtures. Base course — The layer of selected material in a pavement structure placed between a subbase and a surface course. Concrete pavement — The most common form of rigid pavement, in which the top slab is constructed of portland cement concrete. Flexible pavement — A pavement structure that does not distribute traffic load to the subgrade by means of slab action but mainly through spreading of the load by providing sufficient thickness of the pavement structure. Overlay — A new surface layer laid on an existing pavement to improve the latter’s load-carrying capacity. Pavement structure — A structure consisting of one or more layers of selected materials constructed on prepared subgrade to designed strength and thickness(es) for the purpose of supporting traffic. Rigid pavement — A pavement structure that distributes traffic loads to the subgrade by means of slab action through its top layer of high-bending resistance. Subbase — The layer of selected material in a pavement structure placed between the subgrade and the base or surface course. Subgrade — The top surface of graded foundation soil, on which the pavement structure is constructed. Surface course — The top layer of a pavement structure placed on the base course, the top surface of which is in direct contact with traffic loads.
References AASHTO. 1972. AASHTO Interim Guide for Design of Pavement Structures. American Association of State Highway and Transportation Officials, Washington, D.C. AASHTO. 1989. Standard Specifications for Transportation Materials and Methods of Sampling and Testing. Part I and II. American Association of State Highway and Transportation Officials, Washington, D.C. AASHTO. 1993. AASHTO Guides for Design of Pavement Structures. American Association of State Highway and Transportation Officials, Washington, D.C. ACI. 1977. Building Code Requirements for Reinforced Concrete. American Concrete Institute, Detroit, MI.
Highway and Airport Pavement Design
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Asphalt Institute. 1983a. Asphalt Overlays for Highway and Street Rehabilitation. Manual Series No. 17. Lexington, KY. Asphalt Institute. 1983b. Asphalt Technology and Construction Practices. Educational Series ES-I, 2nd ed. Lexington, KY. Asphalt Institute. 1991. Thickness Design — Asphalt Pavements for Highways & Streets. Manual Series No. 1. Lexington, KY. ASTM. 1992. Annual Books of ASTM Standards. American Society for Testing and Materials, Philadelphia, PA. Boussinesq, J. 1885. Application des Potentiels a l’etude de l’equilibre et du Mouvement des Solids Elastiques. Gauthier-Villars, Paris. FAA. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C. Federal Aviation Administration. Fwa, T.F., and Li, S. 1994. Estimation of lane distribution of truck traffic for pavement design. Paper accepted for publication. Journal of Transportation Engineering. Fwa, T.F., Shi, X.P., and Tan, S.A. 1993. Load-Induced Stresses and Deflections in Concrete Pavement — Analysis by Rectangular Thick-Plate Model. CTR Technical Report CTR-93-5. Centre for Transportation Research, Faculty of Engineering, National University of Singapore. Fwa, T.F., and Sinha, K.C. 1985. A Routine Maintenance and Pavement Performance Relationship Model for Highways. Joint Highway Research Project Report JHRP-85-11. Purdue University, West Lafayette, IN. Highway Research Board. 1962. The AASHO Road Test, Report 5 — Pavement Research. HRB Special Report 61E. Washington, D.C. PCA. 1984. Thickness Design for Concrete Highway and Street Pavements. Portland Cement Association, Skokie, IL. Shi, S.P., Tan, S.A., and Fwa, T.F. 1994. Rectangular plate with free edges on a Pasternak foundation. Journal of Engineering Mechanics. 120(5):971–988. Tayabji, S.D. and Okamoto, P.A. 1985. Thickness design of concrete resurfacing. Proc. 3rd Int. Conf. on Concrete Pavement Design and Rehabilitation, April 23–25, Purdue University, West Lafayette, IN, pp. 367–379. Van Til, C.J., McCullough, B.F., Vallerga, B.A., and Hicks, R.G. 1972. Evaluation of AASHO Interim Guides for Design of Pavement Structures. NCHRP Report 128. Highway Research Board, Washington, D.C. Westergaard, H.M. 1926. Stresses in concrete pavements computed by theoretical analysis. Public Roads. 7(2):25–35. Westergaard, H.M. 1933. Analytical tools for judging results of structural tests of concrete pavements. Public Roads. 14(10). Westergaard, H.M. 1948. New formulas for stresses in concrete pavements of airfield. ASCE Transactions. Vol. 113. Yoder, E.J., and Witczak, M.W. 1975. Principles of Pavement Design, 2nd ed. John Wiley & Sons, New York.
Further Information A widely quoted reference to the basics of practical design of highway and airport pavements is Principles of Pavement Design, by E.J. Yoder and M.W. Witczak. Although the described design methods by various agencies are outdated, the book is still a valuable reference on the requirements of pavement construction and design. Detailed descriptions of pavement design methods, pavement material, and construction requirements by various organizations are available in their respective publications. The Asphalt Institute publishes a manual series addressing bituminous pavement-related topics — including thickness design, pavement rehabilitation and maintenance, pavement drainage, hot-mix design, and paving technology. Additional information concerning topics related to portland cement concrete pavement is found in publications by the Portland Cement Association and American Concrete Institute.
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The latest developments in various aspects of pavement design are reported in a number of technical journals in the field. The most important are the Journal of Transportation Engineering, published bimonthly by the American Society of Civil Engineers, and Transportation Research Records, published by the Transportation Research Board. There are about 40 issues of Transportation Research Records published each year, each collecting a group of technical papers addressing a specialized area of transportation engineering. There are several major conferences that focus on highway and airport pavements. The International Conference on Structural Design of Asphalt Pavements has been held once every five years since 1962. The seventh conference, in 1992, was named International Conference on Asphalt Pavements: Design, Construction and Performance to reflect the added scope of the conference. The proceedings of the conferences document advances in areas of asphalt pavement technology. Another conference, the International Conference on Concrete Pavement Design and Rehabilitation, focuses on the development of concrete pavement technology. It has been organized once every four years since 1977 by Purdue University. There is also the International Conference on the Bearing Capacity of Roads and Airfields, held at intervals of four years since 1982. Other related publications are the Proceedings of the World Road Congress, published by the Permanent International Association of Road Congress, and the Proceedings of the Road Congress of the International Road Federation.
