Chapter 1 Introduction
HISTORICAL DEVELOPMENTS Although pavement design has gradually evolved from art to science, empiricism still plays an important role even up to the present day . Prior to the early 1920s, the thickness of pavement was based purely on experience. The same thickness was used for a section of highway even though widely different soils were encountered . As experience was gained throughout the years, various methods were developed by different agencies for determining the thickness of pavement required.
Flexible Pavements Flexible pavements are constructed of bituminous and granular materials . The first asphalt roadway in the United States was constructed in 1870 at Newark, New Jersey . The first sheet-asphalt pavement, which is a hot mixture of asphalt cement with clean , angular, graded sand and mineral filler, was laid in 1876 on Pennsylvania Avenue in Washington, D.C., with imported asphalt from Trinidad Lake. As of 2001 (FHWA , 2001), there are about 2 .5 million miles of paved roads in the United States, of which 94% are asphalt surfaced .
Design Methods Methods of flexible pavement design can be classified into five categories: 1) empirical method with or without a soil strength test, 2) limiting shear failure method, 3) limiting deflection method, 4) regression method based on pavement performance or road test, and 5) mechanistic–empirical method.
Empirical Methods The use of the empirical method without a strength test dates back to the development of the Public Roads (PR) soil classification system (Hogentogler and Terzaghi, 1929), in which the subgrade was classified as uniform from A-1 to A-8 and non uniform from B-1 to B-3 . The PR system was later modified by the Highway Research Board (HRB, 1945), in which soils were grouped from A1 to A- 7 and a group index was added to differentiate the soil within each group .
Steele (1945) discussed the application of HRB classification and group index in estimating the sub - base and total pavement thickness without a strength test . The empirical method with a strength test was first used by the California Highway Department in 1929 (Porter ,1950). The thickness of pavements was related to the California Bearing Ratio (CBR), defined as the penetration resistance of a subgrade soil relative to a standard crush d rock. The CBR method of design was studied extensively by the U .S. Corps of Engineers during World War II and became a very popular method after the war .
Limiting Shear Failure Method The limiting shear failure method is used t o determine the thickness of pavements so that shear failures will not occur . The major properties of pavement components and subgrade soils to be considered are their cohesion and angle of internal friction . Barber (1946) applied Terzaghi's bearing capacity formula (Terzaghi, 1943) to determine pavement thickness . McLeod (1953) advocated the use of logarithmic spirals to determine the bearing capacity of pavements. These methods were reviewed by Yoder (1959) in his book Principles of Pavement Design, but were not even mentioned in the second edition (Yoder and Witczak, 1975) . This is not surprising because, with the ever increasing speed and volume of traffic, pavements should be designed for riding comfort rather than for barely preventing shear failures .
Limiting Deflection Methods The limiting deflection method is used to determine the thickness of pavements so that the vertical deflection will not exceed the allowable limit. The Kansas State Highway Commission(1947)modified Boussinesq's equation (Boussinesq, 1885) and limited the deflection of subgrade to 0.1 in. (2.54 mm). The U.S. Navy (1953) applied Burmister's two-layer theory (Burmister, 1943) and limited the sur - face deflection to 0 .25 in . (6.35 mm) . The use of deflection as a design criterion has the ap parent advantage that it can be easily measured in the field . Unfortunately, pavement failures are caused by excessive stresses and strains instead of deflections.
Regression Methods Based on Pavement Performance or Road Tests A good example of the use of regression equations for pavement design is the AASHTO method based on the results of road tests. The disadvantage of the method is that the design equations can be applied only to the conditions at the road test site. For conditions other than those under which the equations were developed, extensive modifications based on theory or experience are needed .
Regression equations can also be developed from the performance of existing pavements, such as those used in the pavement evaluation systems COPES (Darter et al., 1985) and EXPEAR (Hall et aL,1989) . Unlike pavements subjected to road tests, the materials and construction of these pavements were not well controlled, so a wide scatter of data and a large standard error are expected . Al - though these equations can illustrate the effect of various factors on pavement performance, their usefulness in pavement design is limited because of the many uncertainties involved .
Mechanistic–Empirical Methods The mechanistic–empirical method of design is based on the mechanics of materials that relates an input, such as a wheel load, to an output or pavement response, such as stress or strain . The response values are used to predict distress from laboratory-test and field-performance data. Dependence on observed performance is necessary because theory alone has not proven sufficient to design pavements realistically .
Kerkhoven and Dormon (1953) first suggested the use of vertical compressive strain on the surface of subgrade as a failure criterion to reduce permanent deformation: Saal and Pell (1960) recommended the use of horizontal tensile strain at the bottom of asphalt layer to minimize fatigue cracking, as shown in Figure 1.1. The use of the above concepts for pavement design was first presented in the United States by Dormon and Metcalf (1965).
The term "hot mix asphalt" in Figure 1 .1 is synonymous with the commonly used "asphalt concrete ." It is an asphalt aggregate mixture produced at a batch or drum-mixing facility that must he mixed, spread, and compacted at an elevated temperature .To avoid the confusion between portland cement concrete (PCC) and asphalt concrete (AC) . the term hot mix concrete (HMA) will be used frequently throughout this book in place of asphalt concrete .
Computer Programs Various computer programs based on Burmister's layered theory have been developed . The earliest and the best known is the CHEV program developed by the Chevron Research Company (Warren and Dieckmann, 1963) . The pro -gram can be applied only to linear elastic materials but was modified by the Asphalt Institute in the DAMA program to account for nonlinear elastic granular materials (Hwang and Witczak, 1979) .
Other Computer Programs • LSYM5 • PDMAP (Probabilistic Distress Models for Asphalt Pavements) • DIPLOMAT • ILLI-PAVE • MICH-PAVE
Rigid Pavements Rigid pavements are constructed of Portland cement concrete . The first concrete pavement was built in Bellefontaine, Ohio in 1893 (Fitch, 1996), 15 years earlier than the one constructed in Detroit, Michigan, in 1908, as mentioned in the first edition. As of 2001, there were about 59,000 miles (95,000km) of rigid pavements in the United States. The development of design methods for rigid pavements is not as dramatic as that of flexible pavements, because the flexural stress in concrete has long been considered as a major, or even the only, design factor .
Analytical Solutions Analytical solutions ranging from simple closedform formulas to complex derivations are available for determining the stresses and deflections in concrete pavements .
Goldbeck's Formula By treating the pavement as a cantilever beam with a load concentrated at the corner, Goldbeck (1919) developed a simple equation for the design of rigid pavements, as indicated by Eq.4.12 in Chapter 4. The same equation was applied by Older (1924) in the Bates Road Test .
Westergaard's Analysis Based on Liquid Foundations The most extensive theoretical studies on the stresses and deflections in concrete pavements were made by Westergaard (1926a, 1926b, 1927, 1933, 1939, 1943, 1948), who developed equations due to temperature curling as well as three cases of loading : load applied near the corner of a large slab, load applied near the edge of a large slab but at a considerable distance from any corner, and load applied at the interior of a large slab at a considerable distance from any edge.
• The analysis was based on the simplifying assumption that the re - active pressure between the slab and the subgrade at any given point is proportional to the deflection at that point, independent of the deflections at any other points . This type of foundation is called a liquid or Winkler foundation . Westergaard also assumed that the slab and subgrade were in full contact .
In conjunction with Westergaard's investigation, the U.S. Bureau of Public Roads conducted, at the Arlington Experimental Farm, Virginia, an extensive investigation on the structural behavior of concrete pavements . The results were published in Public Roads from 1935 to 1943 as a series of six papers and reprinted as a single volume for wider distribution (Teller and Sutherland, 1935-1943) .
Pickett's Analysis Based on Solid Foundations In view of the fact that the actual subgrade behaved more like an elastic solid than a dense liquid, Pickett et al. (1951) developed theoretical solutions for concrete slabs on an elastic half-space . The complexities of the mathematics involved have denied this refined method the attention it merits. However, a simple influence chart based on solid foundations was developed by Pickett and Badaruddin (1956) for determining the edge stress, which is presented in Section 5.3.2.
Numerical Solutions All the analytical solutions mentioned above were based on the assumption that the slab and the subgrade are in full contact . It is well known that, due to pumping, temperature curling, and moisture warping, the slab and subgrade are usually not in contact. With the advent of computers and numerical methods, some analyses based on partial contact were developed .
Discrete-Element Methods Hudson and Matlock (1966) applied the discrete- element method by assuming the subgrade to be a dense liquid . The discreteelement method is more or less similar to the finite-difference method in that the slab is seen as an assemblage of elastic joints, rigid bars, and torsional bars . The method was late r extended by Saxena (1973) for analyzing slabs on an elastic solid foundation .
Finite-Element Methods With the development of the powerful finite-element method, a break-through was made in the analysis of rigid pavements . Cheung and Zienkiewicz (1965) developed finite-element methods for analyzing slabs on elastic foundations of both liquid and solid types. The methods were applied to jointed slabs on liquid foundations by Huang and Wang (1973, 1974) and on solid foundations by Huang (1974a) . In collaboration with Huang (Chou and Huang, 1979, 1981, 1982), Chou (1981) developed finite-element computer programs named WESLIQID and WESLAYER for the analysis of liquid and layered foundations, respectively .
The consideration of foundation as a layered system is more realistic when layers of base and subbase exist above the subgrade . Other finiteelement computer programs available include ILLI-SLAB developed at the University of Illinois (Tabatabaie and Barenberg, 1979,1980), JSLAB developed by the Portland Cement Association (Tayabji and Colley, 1986), and RISC developed by Resource International, Inc . (Majidzadeh et al . , 1984) .
The general-purpose 3-D finite-element package ABAQUS (1993) was used in simulating pavements involving nonlinear subgrade under dynamic loading (Zaghloul and White, 1994) and in investigating the effects of discontinuity on the response of a jointed plain concrete pavement under a standard falling weight deflectometer load (Uddin et al., 1995).
Fatigue of Concrete An extensive study was made by the Illinois Division of Highways during the Bates Road Test on the fatigue properties of concrete (Clemmer,1923). It was found that an induced flexural stress could be repeated indefinitely with out causing rupture, provided the intensity of extreme fiber stress did not exceed approximately 50% of the modulus of rupture, and that, if the stress ratio was above 50%, the allowable number of stress repetitions to cause failures decreased drastically as the stress ratio increased .
Although the arbitrary use of 50% stress ratio as a dividing line was not actually proved, this assumption has been used most frequently as a basis for rigid pavement design . To obtain a smoother fatigue curve, the current PCA method assumes a stress ratio of 0.45, below which no fatigue damage need be considered .
Pumping With increasing truck traffic, particularly just before World War II, it became evident that subgrade type played an important role in pavement performance. The phenomenon of pumping, which is the ejection of water and subgrade soils through joints and cracks and along the pavement edge, was first described by Gage (1932). After pavement pumping became critical during the war, rigid pavements were constructed on granular base courses of varying thickness to protect against loss of subgrade support due to pumping. Many studies were made on the design of base courses for the correction of pumping.
Probabilistic Methods The application of probabilistic concepts to rigid pavement design was presented by Kher and Darter(1973), and the concepts were incorporated into the AASHTO design guide (AASHTO, 1986).Huang and Sharpe (1989) developed a finite-element probabilistic computer program for the design of rigid pavements and showed that the use of a cracking index in a reliability context was far superior to the current deterministic approach .
PAVEMENT TYPES There are three major types of pavements :
• Flexible or asphalt pavements. • Rigid or concrete pavements . • Composite pavements .
Conventional Flexible Pavements Conventional flexible pavements are layered systems with better materials on top where the intensity of stress is high and inferior materials at the bottom where the intensity is low. Adherence to this design principle makes possible the use of local materials and usually results in a most economical design. This is particularly true in regions where high-quality materials are expensive but local materials of inferior quality are readily available .
Figure shows the cross section of a conventional flexible pavement . Starting from the top, the pavement consists of seal coat, surface course, tack coat, binder course, prime coat, base course, subbase course, compacted subgrade, and natural subgrade. The use of the various courses is based on either necessity or economy, and some of the courses may be omitted .
Typical cross section of a conventional flexible pavement
Seal Coat Seal coat is a thin asphalt surface treatment used to waterproof the surface or to provide skid resistance where the aggregates in the surface course could be polished by traffic and become slippery . Depending on the purpose, seal coats might or might not be covered with aggregate . Details about skid resistance are presented in Section 9.3 .
Surface Course The surface course is the top course of an asphalt pavement, sometimes called the wearing course. It is usually constructed of dense graded HMA . It must be tough to resist distortion under traffic and provide a smooth and skid-resistant riding surface . It must be waterproof to protect the entire pavement and subgrade from the weakening effect of water . If the above requirements cannot be met, the use of a seal coat is recommended .
Binder Course The binder course, sometimes called the asphalt base course, is the asphalt layer below the surface course. There are two reasons that a binder course is used in addition to the surface course . First, the HMA is too thick to be compacted in one layer, so it must be placed in two layers . Second, the binder course generally consists of larger aggregates and less asphalt and does not require as high a quality as the surface course, so replacing a part of the surface course by the binder course results in a more economical design . If the binder course is more than 3 in. (76 mm), it is generally placed in two layers.
Tack Coat and Prime Coat A tack coat is a very light application of asphalt, usually asphalt emulsion diluted with water, used to ensure a bond between the surface being paved and the overlying course. It is important that each layer in an asphalt pavement be bonded to the layer below. Tack coats are also used to bond the asphalt layer to a PCC base or an old asphalt pavement . The three essential requirements of a tack coat are that it must be very thin, it must uniformly cover the entire surface to be paved, and it must be allowed to break or cure before the HMA is laid .
A prime coat is an application of low-viscosity cutback asphalt to an absorbent surface, such as an untreated granular base on which an asphalt layer will be placed . Its purpose is to bind the granular base to the asphalt layer. The difference between a tack coat and a prime coat is that a tack coat does not require the penetration of asphalt into the underlying layer, whereas a prime coat penetrates into the underlying layer, plugs the voids, and forms a watertight surface. Although the type and quantity of asphalt used are quite different, both are spray applications.
Base Course and Subbase Course The base course is the layer of material immediately beneath the surface or binder course . It can be composed of crushed stone, crushed slag, or other untreated or stabilized materials . The subbase course is the layer of material beneath the base course . The reason that two different granular materials are used is for economy. Instead of using the more expensive base course material for the entire layer, local and cheaper materials can be used as a subbase course on top of the subgrade . If the base course is open graded, the subbase course with more fines can serve as a filter between the subgrade and the base course .
Subgrade The top 6 in . (152 mm) of subgrade should be scarified and compacted to the desirable density near the optimum moisture content . This compacted subgrade may be the in-situ soil or a layer of selected material .
Full-Depth Asphalt Pavements .
Full-depth asphalt pavements are constructed by placing one or more layers of HMA directly on the subgrade or improved subgrade . This concept was conceived by the Asphalt Institute in 1960 and is generally considered the most cost-effective and dependable type of asphalt pavement for heavy traffic . This type of construction is quite popular in areas where local materials are not available. It is more convenient to purchase only one material, i .e ., HMA, rather than several materials from different sources, thus minimizing the administration and equipment costs
shows the typical cross section for a full-depth asphalt pavement . The asphalt base course in the full-depth construction is the same as the binder course in conventional pavement. As with conventional pavement, a tack coat must be applied between two asphalt layers to bind them together .
According to the Asphalt Institute (AI, 1987), fulldepth asphalt pavements have the following advantages : 1) They have no permeable granular layers to entrap water and impair performance . 2) Time required for construction is reduced . On widening projects, where adjacent traffic flow must usually be maintained, full-depth asphalt can be especially advantageous . 3) When placed in a thick lift of 4 in . (102 mm) or more, construction seasons may be extended .
4) They provide and retain uniformity in the pavement structure . 5) They are less affected by moisture or frost . 6) According to limited studies, moisture contents do not build up in subgrades under full-depth asphalt pavement structures as they do under pavements with granular bases . Thus, there is little or no reduction in subgrade strength .
Rigid Pavements Rigid pavements are constructed of portland cement concrete and should be analyzed by the plate theory, instead of the layered theory. Plate theory is a simplified version of the layered theory that assumes the concrete slab to be a medium thick plate with a plane before bending which remains a plane after bending . If the wheel load is applied in the interior of a slab, either plate or layered theory can be used and both should yield nearly the same flexural stress or strain, as discussed in Section 5 .3 .4 .
If the wheel load is applied near to the slab edge, say less than 2 ft (0 .61 m) from the edge, only the plate theory can be used for rigid pavements . The reason that the layered theory is applicable to flexible pavements but not to rigid pavements is that PCC is much stiffer than HMA and distributes the load over a much wider area . Therefore, a distance of 2 ft(0.61 m) from the edge is considered quite far in a flexible pavement but not far enough in a rigid pavement . The existence of joints in rigid pavements also makes the layered theory inapplicable . Details of plate theory are presented in Chapters 4 and 5 .
Figure 1 .4 shows a typical cross section for rigid pavements . In contrast to flexible pavements, rigid pavements are placed either directly on the prepared subgrade or on a single layer of granular or stablized material . Because there is only one layer of material under the concrete and above the subgrade, some call it a base course, others a subbase.
Use of Base Course Early concrete pavements were constructed directly on the subgrade without a base course. As the weight and volume of traffic increased, pumping began to occur, and the use of a granular base course became quite popular . When pavements are subject to a large number of very heavy wheel loads with free water on top of the base course, even granular materials can be eroded by the pulsative action of water . For heavily traveled pavements, the use of a cement-treated or asphalttreated base course has now become a common practice .
Although the use of a base course can reduce the critical stress in the concrete, it is uneconomical to build a base course for the purpose of reducing the concrete stress. Because the strength of concrete is much greater than that of the base course, the same critical stress in the concrete slab can be obtained without a base course by slightly increasing the concrete thickness . The following reasons have been frequently cited for using a base course.
Types of Concrete Pavement Concrete pavements can be classified into four types : 1) jointed plain concrete pavement (JPCP), 2) jointed reinforced concrete pavement (JRCP), 3) continuous reinforced concrete pavement (CRCP), 4) prestressed concrete pavement (PCP) . Except for PCP with lateral prestressing, a longitudinal joint should be installed between two traffic lanes to prevent longitudinal cracking . Figure 1.7 shows the major characteristics of these four types of pavements .
Jointed Plain Concrete Pavements All plain concrete pavements should be constructed with closely spaced contraction joints . Dowels or aggregate interlocks may be used for load transfer across the joints. The practice of using or not using dowels varies among the states . Dowels are used most frequently in the southeastern states, aggregate interlocks in the western and southwestern states, and both are used in other areas.
Depending on the type of aggregate, climate, and prior experience, joint spacings between 15 and 30 ft (4.6 and 9.1 m) have been used . However, as the joint spacing in creases, the aggregate interlock decreases, and there is also an increased risk of cracking . Based on the results of a performance survey, Nussbaum and Lokken (1978) recommended maximum joint spacings of 20 ft (6 .1 m) for doweled joints and 15 ft (4 .6 m) for undoweled joints.
Jointed Reinforced Concrete Pavements Steel reinforcements in the form of wire mesh or deformed bars do not increase the structural capacity of pavements but allow the use of longer joint spacings . This type of pavement is used most frequently in the northeastern and north central part of the United States . Joint spacings vary from 30 to 100 ft (9 .1 to 30 m) . Because of the longer panel length, dowels are required for load transfer across the joints .
The amount of distributed steel in JRCP increases with the increase in joint spacing and is designed to hold the slab together after cracking . However, the number of joints and dowel costs decrease with the increase in joint spacing. Based on the unit costs of sawing, mesh, dowels, and joint sealants, Nussbaum and Lokken (1978) found that the most economical joint spacing was about 40 ft (12 .2 m) . Maintenance costs generally increase with the increase in joint spacing, so the selection of 40 ft (12 .2 m) as the maximum joint spacing appears to be warranted .
Continuous Reinforced Concrete Pavements It was the elimination of joints that prompted the first experimental use of CRCP in 1921 on Columbia Pike near Washington, D.C. The advantages of the joint-free design were widely accepted by many states, and more than two dozen states have used CRCP with a two-lane mileage totaling over 20,000 miles (32,000 km) . It was originally reasoned that joints were the weak spots in rigid pavements and that the elimination of joints would decrease the thickness of pavement required
As a result, the thickness of CRCP has been empirically reduced by 1 to 2 in . (25 to 50 mm) or arbitrarily taken as 70 to 80% of the conventional pavement . The formation of ransverse cracks at relatively close intervals is a distinctive characteristic of CRCP. These cracks are held tightly by the reinforcements and should be of no concern as long as they are uniformly spaced . The distress that occurs most frequently in CRCP is punchout at the pavement edge. This type of distress takes place between two parallel random transverse cracks or at the intersection of Y cracks .
Prestressed Concrete Pavements Concrete is weak in tension but strong in compression. The thickness of concrete pavement required is governed by its modulus of rupture, which varies with the tensile strength of the concrete . The pre-application of a compressive stress to the concrete greatly reduces the tensile stress caused by the traffic loads and thus decreases the thickness of concrete required . The prestressed concrete pavements have less probability of cracking and fewer transverse joints and therefore result in less maintenance and longer pavement life .
Composite Pavements A composite pavement is composed of both HMA and PCC . The use of PCC as a bottom layer and HMA as a top layer results in an ideal pavement with the most desirable characteristics. The PCC provides a strong base and the HMA provides a smooth and nonreflective surface . However, this type of pavement is very expensive and is rarely used as a new construction . As of 2001, there are about 97,000 miles (155,000 km) of composite pavements in the United States, practically all of which are the rehabilitation of concrete pavements using asphalt overlays .
Design Methods When an asphalt overlay is placed over a concrete pavement, the major load-carrying component is the concrete, so the plate theory should be used . Assuming that the HMA is bonded to the concrete, an equivalent section can be used with the plate theory to determine the flexural stress in the concrete slab, as is described in Section 5 .1 .2 . If the wheel load is applied near to the pavement edge or joint, only the plate theory can be used . If the wheel load is applied in the interior of the pavement far from the edges and joints, either layered or plate theory can be used .
• The concrete pavement can be either JPCP, JRCP, or CRCP. Composite pavements also include asphalt pavements with stabilized bases . For flexible pavements with untreated bases, the most critical tensile stress or strain is located at the bottom of the asphalt layer ; for asphalt pavements with stabilized bases, the most critical location is at the bottom of the stabilized bases.
Pavement Sections The design of composite pavements varies a great deal . Figure 1 . 8 shows two different cross sections that have been used. Section (a) (Ryell and Corkill , 1973) shows the HMA placed directly on the PCC base, which is a more conventional type of construction . A disadvantage of this construction is the occurrence of reflection cracks on the asphalt surface that are due to the joints and cracks in the concrete base . The open-graded HMA serves as a buffer to reduce the amount of reflection cracking .
Placing thick layers of granular materials between the concrete base and the asphalt layer, as in Section (b) (Baker, 1973), can eliminate reflection cracks, but the placement of a stronger concrete base under a weaker granular material can be an ineffective design. The use of a 6-in . (152-mm) densegraded crushed-stone base beneath the more rigid macadam base, consisting of 2 .5-in. (64-mm) stone choked with stone screenings,prevents reflection cracking . The 3 .5-in. (89-mm) HMA is composed of a 1 .5-in . (38-mm) surface course and a 2-in . (51-mm) binder course . Figure 1 .9 shows the composite structures recommended for premium pavements (Von Quintus et al., 1980) . Section (a) shows the composite pavement with a jointed plain concrete base, and Section (b) shows the composite pavement with a continuous reinforced
DESIGN FACTORS Design factors can be divided into four broad categories : traffic and loading, environment, materials, and failure criteria . The factors to be considered in each category will be escribed, and how the design process fits into an overall pavement management system will be discussed .
DESIGN FACTORS Design factors can be divided into four broad categories : traffic and loading, environment, materials, and failure criteria . The factors to be considered in each category will be described, and how the design process fits into an overall pavement management system will be discussed.
Axle Loads the wheel spacing for a typical semitrailer consisting of single axle with single tires, single axle with dual tires, and tandem axles with dual tires. For special heavy-duty haul trucks, tridem axles consisting of a set of three axles, each spaced at 48 to 54 in. (1.22 to 1 .37 m) apart, also exist.
• The design may be unsafe if the tandem and tridem axles are treated as a group and considered as one repetition. The design is too conservative if each axle is treated independently and considered as one repetition. In the design of flexible pavements by layered theory, only the wheels on one side, say at the outer wheelpath, need be considered; in the design of rigid pavements by plate theory, the wheels on both sides, even at a distance of more than 6 ft (1.8 m) apart, are usually considered
Number of Repetitions With the use of a high-speed computer, it is no problem to consider the number of load repetitions for each axle load and evaluate its damage. The method of dividing axle loads into a number of groups has been used frequently for the design of rigid pavements, as illustrated by the PCA method in Section 12.2.However, its application to flexible pavements is not widespread, because of the empirical nature of the design and of the large amount of computer time required.
Instead of analyzing the stresses and strains due to each axle-load group, a simplified and widely accepted procedure is to develop equivalent factors and convert each load group into an equivalent 18-kip (80-kN) single-axle load, as illustrated by the Asphalt Institute method in Section 11.2 and the AASHTO method in Sections 11 . 3 and 12.3.
• It should be noted that the equivalency between two different loads depends on the failure criterion employed. Equivalent factors based on fatigue cracking could be different from those based on permanent deformation. Therefore, the use of a single equivalent factor for analyzing different types of distress is empirical and should be considered as approximate only
Contact Area In the mechanistic method of design, it is necessary to know the contact area between tire and pavement, so the axle load can be assumed to be uniformly distributed over the contact area. The size of contact area depends on the contact pressure. As indicated by Figure 1.13, the contact pressure is greater than the tire pressure for lowpressure tires,
because the wall of tires is in compression and the sum of vertical forces due to wall and tire pressure must be equal to the force due to contact pressure; the contact pressure is smaller than the tire pressure for high-pressure tires ,because the wall of tires is in tension. However, in pavement design, the contact pres-sure is generally assumed to be equal to the tire pressure. Because heavier axle loads have higher tire pressures and more destructive effects on pavements, the use of tire pressure as the contact pressure is therefore on the safe side
Heavier axle loads are always applied on dual tires. Figure 1.14a shows the approximate shape of contact area for each tire, which is composed of a rectangle and two semicircles. By assuming length L and width 0.6L, the area of contact
in which Ac = contact area, which can be obtained by dividing the load on each tire by the tire pressure.
• The contact area shown in Figure 1.14a was used previously by PCA (1966) for the design of rigid pavements. The current PCA (1984) method is based on the finite element procedure, and a rectangular area is assumed with length 0.8712L and width 0.6L, which has the same area of 0.5227L2, as shown in Figure 1.14b. These contact areas are not axisymmetric and cannot be used with the layered theory. When the
