Geometric design deals with the dimensioning of the elements of highways, such

CHAPTER 15 Geometric Design of Highway Facilities Geometric design deals with the dimensioning of the elements of highways, such as vertical and horizontal curves, cross sections, truck climbing lanes, bicycle paths, and parking facilities. The characteristics of driver, pedestrian, vehicle, and road, as discussed in Chapter 3, serve as the basis for determining the physical dimensions of these elements. For example, lengths of vertical curves or radii of circular curves are determined to assure that the minimum stopping sight distance is provided to highway users for the design speed of the highway. The fundamental objective of geometric design is to produce a smooth-flowing and safe highway facility, an objective that only can be achieved by providing a consistent design standard that satisfies the characteristics of the driver and the vehicles that use the road. The American Association of State Highway and Transportation Officials (AASHTO) serves a critical function in developing guidelines and standards used in highway geometric design. The membership of AASHTO includes representatives from every state highway and transportation department in the U.S. as well as the Federal Highway Administration (FHWA). The association has several technical committees that consider suggested standards from individual states. When a standard is approved, it is adopted and used by the member states. The AASHTO publication A Policy on Geometric Design of Highways and Streets provides the standards for geometric design of highways. In this chapter, the principles and theories used in the design of horizontal and vertical alignments are presented together with the current standards used for geometric design, as recommended by AASHTO. Design principles and standards are also linked to the characteristics of the driver, pedestrian, vehicle, and road, as discussed in Chapter 3. 737

738 Part 4 Location, Geometrics, and Drainage 15.1 FACTORS INFLUENCING HIGHWAY DESIGN Highway design is based on specified design standards and controls which depend on the following roadway system factors: Functional classification Design hourly traffic volume and vehicle mix Design speed Design vehicle Cross section of the highway, such as lanes, shoulders, and medians Presence of heavy vehicles on steep grades Topography of the area that the highway traverses Level of service Available funds Safety Social and environmental factors These factors are often interrelated. For example, design speed depends on functional classification which is usually related to expected traffic volume. The design speed may also depend on the topography, particularly in cases where limited funds are available. In most instances, the principal factors used to determine the standards to which a particular highway will be designed are the level of service to be provided, expected traffic volume, design speed, and the design vehicle. These factors, coupled with the basic characteristics of the driver, vehicle, and road, are used to determine standards for the geometric characteristics of the highway, such as cross sections and horizontal and vertical alignments. For example, appropriate geometric standards should be selected to maintain a desired level of service for a known proportional distribution of different types of vehicles. 15.1.1 Highway Functional Classification Highways are classified according to their functions in terms of the service they provide. The classification system facilitates a systematic development of highways and the logical assignment of highway responsibilities among different jurisdictions. Highways and streets are categorized as rural or urban roads, depending on the area in which they are located. This initial classification is necessary because urban and rural areas have significantly different characteristics with respect to the type of land use and population density, which in turn influences travel patterns. Within the classification of urban and rural, highways are categorized into the following groups: Principal arterials Minor arterials Major collectors Minor collectors Local roads and streets Freeways are not listed as a separate functional class since they are generally classified as part of the principal arterial system. However, they have unique geometric criteria that require special design consideration.

Chapter 15 Geometric Design of Highway Facilities 739 Functional System of Urban Roads Urban roads comprise highway facilities within urban areas as designated by responsible state and local officials to include communities with a population of at least 5000 people. Some states use other values, for example, the Virginia Department of Transportation uses a population of 3500 to define an urban area. Urban areas are further subdivided into urbanized areas with populations of 50,000 or more and small urban areas with populations between 5000 and 50,000. Urban roads are functionally classified into principal arterials, minor arterials, collectors, and local roads. A schematic of urban functional classification is illustrated in Figure 15.1 for a suburban environment. Urban Principal Arterial System. This system of highways serves the major activity centers of the urban area and consists mainly of the highest-traffic-volume corridors. It carries a high proportion of the total vehicle-miles of travel within the urban area Figure 15.1 Schematic Illustration of the Functional Classes for a Suburban Road Network SOURCE: A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D.C., 2004. Used with permission.

740 Part 4 Location, Geometrics, and Drainage including most trips with an origin or destination within the urban area. The system also serves trips that bypass the central business districts (CBDs) of urbanized areas. All controlled-access facilities are within this system, although controlled access is not necessarily a condition for a highway to be classified as an urban principal arterial. Highways within this system are further divided into three subclasses based mainly on the type of access to the facility: (1) interstate, with fully-controlled access and gradeseparated interchanges; (2) expressways, which have controlled access but may also include at-grade intersections; and (3) other principal arterials (with partial or no controlled access). Urban Minor Arterial System. Streets and highways that interconnect with and augment the urban primary arterials are classified as urban minor arterials. This system serves trips of moderate length and places more emphasis on land access than the primary arterial system. All arterials not classified as primary are included in this class. Although highways within this system may serve as local bus routes and may connect communities within the urban areas, they do not normally go through identifiable neighborhoods. The spacing of minor arterial streets in fully developed areas is usually not less than 1 mile, but the spacing can be 2 to 3 miles in suburban fringes. Urban Collector Street System. The main purpose of streets within this system is to collect traffic from local streets in residential areas or in CBDs and convey it to the arterial system. Thus, collector streets usually go through residential areas and facilitate traffic circulation within residential, commercial, and industrial areas. Urban Local Street System. This system consists of all other streets within the urban area that are not included in the three systems described earlier. The primary purposes of these streets are to provide access to abutting land and to the collector streets. Through traffic is discouraged on these streets. Functional System of Rural Roads Highway facilities outside urban areas comprise the rural road system. These highways are categorized as principal arterials, minor arterials, major collectors, minor collectors, and locals. Figure 15.2 is a schematic illustration of a functionally classified rural highway network. Rural Principal Arterial System. This system consists of a network of highways that serves most of the interstate trips and a substantial amount of intrastate trips. Virtually all highway trips between urbanized areas and a high percentage of trips between small urban areas with populations of 25,000 or more are made on this system. The system is further divided into freeways (which are divided highways with fully controlled access and no at-grade intersections) and other principal arterials not classified as freeways. Rural Minor Arterial System. This system of roads augments the principal arterial system in the formation of a network of roads that connects cities, large towns, and other traffic generators, such as large resorts. Travel speeds on these roads are relatively high with minimum interference to through movement.

Chapter 15 Geometric Design of Highway Facilities 741 Figure 15.2 Schematic Illustration of a Functionally Classified Rural Highway Network SOURCE: A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D.C., 2004. Used with permission. Rural Collector System. Highways within this system carry traffic primarily within individual counties, and trip distances are usually shorter than those on the arterial roads. This system of roads is subdivided into major collector roads and minor collector roads. Rural Major Collector System. Routes under this system carry traffic primarily to and from county seats and large cities that are not directly served by the arterial system. The system also carries the main intracounty traffic. Rural Minor Collector System. This system consists of routes that collect traffic from local roads and convey it to other facilities. One important function of minor collector roads is that they provide linkage between rural hinterland and locally important traffic generators such as small communities. Rural Local Road System. This system consists of all roads within the rural area not classified within the other systems. These roads serve trips of relatively short distances and connect adjacent lands with the collector roads.

742 Part 4 Location, Geometrics, and Drainage 15.1.2 Highway Design Standards Selection of the appropriate set of geometric design standards is the first step in the design of any highway. This is essential because no single set of geometric standards can be used for all highways. For example, geometric standards that may be suitable for a scenic mountain road with low average daily traffic (ADT) are inadequate for a freeway carrying heavy traffic. The characteristics of the highway should therefore be considered in selecting the geometric design standards. Design Hourly Volume The design hourly volume (DHV) is the projected hourly volume that is used for design. This volume is usually taken as a percentage of the expected ADT on the highway. Figure 15.3 shows the relationship between the highest hourly volumes and ADT. This relationship was computed from the analysis of traffic count data over a wide range of volumes and geographic conditions. For example, Figure 15.3 shows that an hourly volume equal to 12 percent of the ADT is exceeded at 85 percent of locations during 20 hours in the entire year. This curve also shows that between 0 and 20 of the hours with the highest traffic volumes, a small increase in that number of hours results in a significant reduction in the percentage of ADT, whereas a relatively large increase in number of hours greater than the 30th-highest hour results in only a slight decrease in the percentage of ADT. This peculiar characteristic of the curve suggests that it is Figure 15.3 Highways Relationship between Peak Hour and Annual Average Daily Traffic on Rural SOURCE: A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D.C., 2004. Used with permission.

Chapter 15 Geometric Design of Highway Facilities 743 uneconomical to select a DHV greater than that which will be exceeded during 29 hours in a year. Thus, the 30th-highest hourly volume is usually selected as the DHV. Experience has also shown that the 30th-highest hourly volume as a percentage of ADT varies only slightly from year to year, even when significant changes of ADT occur. It has also been shown that, excluding rural highways with unusually high or low fluctuation in traffic volume, the 30th-highest hourly volume for rural highways is usually between 12 and 18 percent of the ADT, with the average being 15 percent. The 30th-highest hourly volume should not be indiscriminately used as the DHV, particularly on highways with unusual or high seasonal fluctuation in the traffic flow. Although the percentage of annual average daily traffic (AADT) represented by the 30th-highest hourly volume on such highways may not be significantly different from those on most rural roads, this criterion may not be applicable, since the seasonal fluctuation results in a high percentage of high-volume hours and a low percentage of low-volume hours. For example, economic consideration may not permit the design to be carried out for the 30th-highest hourly volume, but at the same time, the design should not be such that severe congestion occurs during peak hours. A compromise is to select a DHV that will result in traffic operating at a somewhat slightly lower level of service than that which normally exists on rural roads with normal fluctuations. For this type of rural road, it is desirable to select 50 percent of the volume that occurs for only a few peak hours during the design year as the DHV, even though this may not be equal to the 30th-highest hourly volume. This may result in some congestion during the peak hour, but the capacity of the highway normally will not be exceeded. The 30th-highest hourly volume may also be used as the DHV for urban highways. It is usually determined by applying between 8 and 12 percent to the ADT. However, other relationships may be used for highways with seasonal fluctuation in traffic flow much different from that on rural roads. One alternative is to use the average of the highest afternoon peak hour volume for each week in the year as the DHV. Design Speed Design speed is defined as a selected speed to determine the various geometric features of the roadway. Design speed depends on the functional classification of the highway, the topography of the area in which the highway is located, and the land use of the adjacent area. For highway design, topography is generally classified into three groups: level, rolling, and mountainous terrain. Level terrain is relatively flat. Horizontal and vertical sight distances are generally long or can be achieved without much construction difficulty or major expense. Rolling terrain has natural slopes that often rise above and fall below the highway grade with occasional steep slopes that restrict the normal vertical and horizontal alignments. Mountainous terrain has sudden changes in ground elevation in both the longitudinal and transverse directions, thereby requiring frequent hillside excavations to achieve acceptable horizontal and vertical alignments. The design speed selected should be consistent with the speed that motorists will expect to drive. For example, a low design speed should not be selected for a rural collector road solely because the road is located in an area of flat topography, since motorists will tend to drive at higher speeds. The average trip length on the highway

744 Part 4 Location, Geometrics, and Drainage is another factor that should be considered in selecting the design speed. In general, highways with longer average trips should be designed for higher speeds. Design speeds range from 20 mi/h to 70 mi/h, with intermediate values of 5 mi/h increments. Design elements show little difference when increments are less than 10 mi/h but exhibit very large differences with increments of 15 mi/h or higher. In general, however, freeways are designed for 60 to 70 mi/h, whereas design speeds for other arterial roads range from 30 mi/h to 60 mi/h. Table 15.1 provides design speed ranges for rural collector roads based on design volume, and Table 15.2 provides recommended values for minimum design speed ranges for various functional classifications. Table 15.1 Minimum Design Speeds for Rural Collector Roads Design Speed (mi /h) for Specified Design Volume (veh /day) Type of Terrain 0 to 400 400 to 2000 Over 2000 Level 40 50 60 Rolling 30 40 50 Mountainous 20 30 40 Note: Where practical, design speeds higher than those shown should be considered. SOURCE: Adapted from A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D.C., 2004. Used with permission. Table 15.2 Minimum Design Speeds for Various Functional Classifications Speed (mi /h) Class 20 30 40 50 60 70 Rural principal arterial Min 50 mi/h for freeways x x x x Rural minor arterial x x x x DHV over 400 x x x Rural DHV 20-400 x x x Collector DHV 100-200 x x x Road Current ADT over 400 x x x Current ADT under 400 x x x DHV over 400 x x x DHV 200-400 x x x Rural DHV 100-200 x x x Local Current ADT over 400 x x x Road Current ADT 250-400 x x x Current ADT 50-250 x x Current ADT under 50 x x Urban principal arterial Minimum 50 mi/h for x x x x x freeways Urban minor arterial x x x x Urban collector street x x x Urban local street x x SOURCE: Road Design Manual, Virginia Department of Transportation, Richmond, VA. (See www.virginiadot.org/business/locdes/rdmanual-index.asp for most current version.)

Chapter 15 Geometric Design of Highway Facilities 745 A design speed is selected to achieve a desired level of operation and safety on the highway. It is one of the first parameters selected in the design process because of its influence on other design variables. Design Vehicle A design vehicle is selected to represent all vehicles on the highway. Its weight, dimensions, and operating characteristics are used to establish the design standards of the highway. The different classes of vehicles and their dimensions were discussed in Chapter 3. The vehicle type selected as the design vehicle is the largest that is likely to use the highway with considerable frequency. The selected design vehicle is used to determine critical design features such as radii at intersections and turning roadways as well as highway grades. The following guidelines apply when selecting a design vehicle: When a parking lot or a series of parking lots are the main traffic generators, the passenger car may be used. For the design of intersections at local streets and park roads, a single-unit truck may be used. At intersections of state highways and city streets that serve buses with relatively few large trucks, a city transit bus may be used. At intersections of highways and low-volume county highways or township/local roads with less than 400 ADT, either an 84-passenger large school bus 40 ft long or a 65-passenger conventional bus 36 ft long may be used. The selection of either of these will depend on the expected usage of the facility. At intersections of freeway ramp terminals and arterial crossroads, and at intersections of state highways and industrialized streets that carry high volumes of traffic, the minimum size of the design vehicle should be WB-20. Cross-Section Elements The principal elements of a highway cross section consist of the travel lanes, shoulders, and medians (for some multilane highways). Marginal elements include median and roadside barriers, curbs, gutters, guard rails, sidewalks, and side slopes. Figure 15.4 shows a typical cross section for a two-lane highway, and Figure 15.5 on the next page shows that for a multilane highway. Figure 15.4 Typical Cross Section for Two-Lane Highways

746 Part 4 Location, Geometrics, and Drainage Figure 15.5 Typical Cross Section for Multilane Highways (half section) Width of Travel Lanes. Travel lane widths usually vary from 9 to 12 ft. Most arterials have 12-ft travel lanes since the extra cost for constructing 12-ft lanes over 10-ft lanes is usually offset by the lower maintenance cost for shoulders and pavement surface, resulting in a reduction of wheel concentrations at the pavement edges. On twolane, two-way rural roads, lane widths of 10 ft or 11 ft may be used, but two factors must be considered when selecting a lane width less than 12 ft wide. When pavement surfaces are less than 22 ft, the crash rates for large trucks tend to increase and, as the lane width is reduced from 12 ft, the capacity of a highway significantly decreases. Lane widths of 10 ft are therefore used only on low-speed facilities. Lanes that are 9 ft wide are used occasionally in urban areas if traffic volume is low and there are extreme right-of-way constraints. Shoulders. The shoulder of a pavement cross section is always contiguous with the traveled lane so as to provide an area along the highway for vehicles to stop when necessary. In some cases, bicycles are permitted to use a highway shoulder particularly on rural and collector roads. Shoulder surfaces range in width from 2 ft on minor roads to 12 ft on major arterials. Shoulders are also used to laterally support the pavement structure. The shoulder width is known as either graded or usable, depending on the section of the shoulder being considered. The graded shoulder width is the whole width of the shoulder measured from the edge of the traveled pavement to the intersection of the shoulder slope and the plane of the side slope. The usable shoulder width is that part of the graded shoulder that can be used to accommodate parked vehicles. The usable width is the same as the graded width when the side slope is equal to or flatter than 4:1 (horizontal:vertical), as the shoulder break is usually rounded to a width between 4 ft and 6 ft, thereby increasing the usable width. When a vehicle stops on the shoulder, it is desirable for it to be at least 1 ft and preferably 2 ft from the edge of the pavement. Based on this consideration, usable shoulder widths should be at least 10 ft on highways having a large number of trucks and on highways with heavy traffic volumes and high speeds. However, it may not always be feasible to provide this minimum width, particularly when the terrain is difficult or when traffic volume is low. A minimum shoulder width of 2 ft may therefore be used on the lowest type of highways, but 6 to 8 ft widths should preferably be used. When pedestrians and bicyclists are permitted, the minimum shoulder width

Chapter 15 Geometric Design of Highway Facilities 747 should be 4 ft. The width for usable shoulders within the median for divided arterials having two lanes in each direction may be reduced to 3 ft, since drivers rarely use the median shoulder for stopping on these roads. The usable median shoulder width for divided arterials with three or more lanes in each direction should be at least 8 ft, since drivers in the lane next to the median often find it difficult to maneuver to the outside shoulder when there is a need to stop. All shoulders should be flush with the edge of the traveled lane and sloped to facilitate drainage of surface water on the traveled lanes. Recommended slopes are 2 to 6 percent for bituminous and concrete-surfaced shoulders, and 4 to 6 percent for gravel or crushed-rock shoulders. Rumble strips may be used on paved shoulders along arterials as a safety measure to warn motorists that they are leaving the traffic lane. Medians. A median is the section of a divided highway that separates the lanes in opposing directions. The width of a median is the distance between the edges of the inside lanes, including the median shoulders. The functions of a median include: Providing a recovery area for out-of-control vehicles Separating opposing traffic Providing stopping areas during emergencies Providing storage areas for left-turning and U-turning vehicles Providing refuge for pedestrians Reducing the effect of headlight glare Providing temporary lanes and cross-overs during maintenance operations Medians can either be raised, flush, or depressed. Raised medians are frequently used in urban arterial streets because they facilitate the control of left-turn traffic at intersections by using part of the median width for left-turn-only lanes. Some disadvantages associated with raised medians include possible loss of control of the vehicle by the driver if the median is accidentally struck, and they cast a shadow from oncoming headlights, which results in drivers finding it difficult to see the curb. Flush medians are commonly used on urban arterials. They can also be used on freeways, but with a median barrier. To facilitate drainage of surface water, the flush median should be crowned. The practice in urban areas of converting flush medians into two-way left-turn lanes is common, since the capacity of the urban highway is increased while maintaining some features of a median. Depressed medians are generally used on freeways and are more effective in draining surface water. A side slope of 6:1 is suggested for depressed medians, although a slope of 4:1 may be adequate. Median widths vary from a minimum of 4 to 80 ft or more. Median widths should be as wide as possible but should be balanced with other elements of the cross section and the cost involved. In general, the wider the median, the more effective it is in providing safe operating conditions and a recovery area for out-of-control vehicles. A minimum width of 10 ft is recommended for use on four-lane urban freeways, which is adequate for two 4-ft shoulders and a 2-ft median barrier. A minimum of 22 ft, preferably 26 ft, is recommended for six or more lanes of freeway. Median widths for urban collector streets vary from 2 to 40 ft, depending on the median treatment. For example, when the median is a paint-striped separation,

748 Part 4 Location, Geometrics, and Drainage 2 to 4 ft medians are required. For narrow raised or curbed areas, 2 to 6 ft medians are required, and for curbed sections, 16 to 40 ft. The larger width is necessary for curbed sections because it provides space for protecting vehicles crossing an intersection and also can be used for landscape treatment. Roadside and Median Barriers. A median barrier is defined as a longitudinal system used to prevent an errant vehicle from crossing the portion of a divided highway separating the traveled ways for traffic in opposite directions. Roadside barriers, on the other hand, protect vehicles from obstacles or slopes on the roadside. They also may be used to shield pedestrians and property from the traffic stream. The provision of median barriers must be considered when traffic volumes are high and when access to multilane highways and other highways is only partially controlled. However, when the median of a divided highway has physical characteristics that may create unsafe conditions, such as a sudden lateral drop-off or obstacles, the provision of a median barrier should be considered regardless of the traffic volume or the median width. Roadside barriers should be provided whenever conditions exist requiring the protection for vehicles along the side of the road. For example, when the slope of an embankment is high or when traveling under an overhead bridge, the provision of a roadside barrier is warranted. There are a wide variety of roadside barriers and the selection of the most desirable system should provide the required degree of shielding at the lowest cost for the specific application. Figure 15.6 illustrates a steel-backed timber guard rail developed as an aesthetic alternative to conventional guardrail systems. Median barriers can be composed of cable or post and beam systems or concrete. For major arterials, concrete barriers are commonly used because of their low life-cycle cost, effective performance, and easy maintenance. Figure 15.7 on page 750 depicts a single-slope concrete median barrier along a rural interstate highway. The primary advantage to this barrier shape is that adjacent pavement can be overlaid several times without affecting its performance. Additional information on selecting, locating, and designing roadside and median barriers can be obtained from the AASHTO Roadside Design Guide. Curbs and Gutters. Curbs are raised structures made of either Portland cement concrete or bituminous concrete (rolled asphalt curbs) that are used mainly on urban highways to delineate pavement edges and pedestrian walkways. Curbs are also used to control drainage, improve aesthetics, and reduce right of way. Curbs can be generally classified as either vertical or sloping. Vertical curbs, (which may be vertical or nearly vertical), range in height from 6 to 8 with steep sides, and are designed to prevent vehicles from leaving the highway. Sloping curbs are designed so that vehicles can cross them if necessary. Figure 15.8 on page 751 illustrates typical highway curbs. Both vertical and sloping curbs may be designed separately or as integral parts of the pavement. In general, vertical curbs should not be used in conjunction with traffic barriers, such as bridge railings or median and roadside barriers, because they could contribute to vehicles rolling over the traffic barriers. Vertical curbs should also be avoided on highways with design speeds greater than 40 mi/h, because at such speeds it is usually difficult for drivers to retain control of the vehicle after an impact with the curb.

Chapter 15 Geometric Design of Highway Facilities 749 Figure 15.6 Steel-Backed Timber Guardrail SOURCE: Roadside Design Guide, American Association of State Highway and Transportation Officials, Washington, D.C., 2006. Used with permission. Gutters or drainage ditches are usually located on the pavement side of a curb to provide the principal drainage facility for the highway. They are sloped to prevent any hazard to traffic, and they usually have cross slopes of 5 to 8 percent and are 1 to 6 ft wide. Gutters can be designed as V-type sections or as broad, flat, rounded sections. Guard Rails. Guard rails are longitudinal barriers placed on the outside of sharp curves and at sections with high fills. Their main function is to prevent vehicles from leaving the roadway. They are installed at embankments higher than 8 ft and when shoulder slopes are greater than 4:1. Shapes commonly used include the W beam and the box beam. The weak post system provides for the post to collapse on impact, with the rail deflecting and absorbing the energy due to impact. Sidewalks. Sidewalks are usually provided on roads in urban areas, but are uncommon in rural areas. Nevertheless, the provision of sidewalks in rural areas should be evaluated during the planning process to determine sections of the road

750 Part 4 Location, Geometrics, and Drainage Figure 15.7 Single-Slope Concrete Median Barrier SOURCE: Roadside Design Guide, American Association of State Highway and Transportation Officials, Washington, D.C., 2006. Used with permission. where they are required. For example, rural principal arterials may require sidewalks in areas with high pedestrian concentrations, such as adjacent to schools, industrial plants, and local businesses. Generally, sidewalks should be provided when pedestrian traffic is high along main or high-speed roads in either rural or urban areas. When shoulders are not provided on arterials, sidewalks are necessary even when pedestrian traffic is low. In urban areas, sidewalks should also be provided along both sides of collector streets that serve as pedestrian access to schools, parks, shopping centers, and transit stops, and along collector streets in commercial areas. Sidewalks should have a minimum clear width of 4 ft in residential areas and a range of 4 to 8 ft in commercial areas. To encourage pedestrians to use sidewalks, they should have all-weather surfaces since pedestrians will tend to use traffic lanes rather than unpaved sidewalks. Cross Slopes. Pavements on straight sections of two-lane and multilane highways without medians are sloped from the middle downward to both sides of the highway, resulting in a transverse or cross slope, with a cross section shape that can be curved, plane or a combination of the two. A parabola is generally used for curved cross sections, and the highest point of the pavement (called the crown) is slightly rounded, with the cross slope increasing toward the pavement edge. Plane cross slopes

Chapter 15 Geometric Design of Highway Facilities 751 Figure 15.8 Typical Highway Curbs SOURCE: A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D.C., 2004. Used with permission. consist of uniform slopes at both sides of the crown. The curved cross section has one advantage which is that the slope increases outward to the pavement edge, thereby enhancing the flow of surface water away from the pavement. A disadvantage is they are difficult to construct. Cross slopes on divided highways are provided by either crowning the pavement in each direction, as shown in Figure 15.9(a) on page 752, or by sloping the entire pavement in one direction, as shown in Figure 15.9(b). The advantage of sloping the pavement in each direction is that surface water is quickly drained away from the traveled roadway during heavy rain storms, whereas the disadvantage is that additional drainage facilities, such as inlets and underground drains, are required. This method is mainly used at areas with heavy rain and snow. In determining the rate of cross slope for design, two conflicting factors should be considered. Although a steep cross slope is required for drainage purposes, it may be undesirable since vehicles will tend to drift to the edge of the pavement, particularly under icy conditions. Recommended rates of cross slopes are 1.5 to 2 percent for hightype pavements and 2 to 6 percent for low-type pavements. High-type pavements have wearing surfaces that can adequately support the expected traffic load without visible distress due to fatigue and are not susceptible to weather conditions. Low-type pavements are used mainly for low-cost roads and have wearing surfaces ranging from untreated loose material to surface-treated earth.

752 Part 4 Location, Geometrics, and Drainage Figure 15.9 Basic Cross Slope Arrangements for Divided Highways SOURCE: A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D.C., 2004. Used with permission. Figure 15.10 Designation of Roadside Regions SOURCE: A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D.C., 2004. Used with permission. Side Slopes. Side slopes are provided on embankments and fills to provide stability for earthworks. They also serve as a safety feature by providing a recovery area for out-of-control vehicles. When being considered as a safety feature, the important sections of the cross slope are the hinge point, the foreslope, and the toe of the slope, as shown in Figure 15.10. The hinge point should be rounded since it is potentially hazardous and may cause vehicles to become airborne while crossing it, resulting in

Table 15.3 Guide for Earth Slope Design Chapter 15 Geometric Design of Highway Facilities 753 Earth Slope, for Type of Terrain Height of Cut or Flat or Moderately Fill (ft) Rolling Steep Steep 0 4 6:1 6:1 4:1 4 10 4:1 4:1 2:1* 10 15 4:1 2.50:1 1.75:1* 15 20 2:1* 2:1* 1.75:1* Over 20 2:1* 2:1* 1.75:1* *Slopes 2:1 or steeper should be subject to a soil stability analysis and should be reviewed for safety. SOURCE: Roadside Design Guide, American Association of State Highway and Transportation Officials, Washington, D.C., 2002. Used with permission. loss of control of the vehicle. The foreslope serves principally as a recovery area, where vehicle speeds can be reduced and other recovery maneuvers taken to regain control of the vehicle. The gradient of the foreslope should therefore not be high. Slopes of 3:1 (horizontal:vertical) or flatter are generally used for high embankments. This can be increased based on conditions at the site. Recommended values for foreslopes and backslopes are provided in Table 15.3. As illustrated in Figure 15.10, the toe of slope is rounded up in order to facilitate the safe movement of vehicles from the foreslope to the backslope. Right of Way. The right of way is the total land area acquired for the construction of a highway. The width should be sufficient to accommodate all the elements of the highway cross section, any planned widening of the highway, and public-utility facilities that will be installed along the highway. In some cases, the side slopes may be located outside the right of way on easement areas. The right of way for twolane urban collector streets should be between 40 and 60 ft, whereas the desirable minimum for two-lane arterials is 84 ft. Right-of-way widths for undivided four-lane arterials vary from 64 to 108 ft, whereas for divided arterials, they range from about 120 to 300 ft, depending on the numbers of lanes and whether frontage roads are included. The minimum right-of-way widths for freeways depend on the number of lanes and the existence of a frontage road. Maximum Highway Grades The effect of grade on the performance of heavy vehicles was discussed in Chapter 3, where it was shown that the speed of a heavy vehicle can be significantly reduced if the grade is steep and/or long. In Chapter 9, it was noted that steep grades affect not only the performance of heavy vehicles but also the performance of passenger cars. In order to limit the effect of grades on vehicular operation, the maximum grade on any highway should be selected judiciously. The selection of maximum grades for a highway depends on the design speed and the design vehicle. It is generally accepted that grades of 4 to 5 percent have little or no effect on passenger cars, except for those with high weight /horsepower ratios,

754 Part 4 Location, Geometrics, and Drainage such as those found in compact and subcompact cars. As the grade increases above 5 percent, however, speeds of passenger cars decrease on upgrades and increase on downgrades. Grade has a greater impact on trucks than on passenger cars. Extensive studies have been conducted, and results (some of which were presented in Chapter 9) have shown that truck speed may increase up to 5 percent on downgrades and decrease by 7 percent on upgrades, depending on the percent and length of the grade. The impact of grades on recreational vehicles is more significant than that for passenger cars, but it is not as critical as that for trucks. However, it is very difficult to establish maximum grades for recreational routes, and it may be necessary to provide climbing lanes on steep grades when the percentage of recreational vehicles is high. Maximum grades have been established based on the operating characteristics of the design vehicle on the highway. These vary from 5 percent for a design speed of 70 mi/h to between 7 and 12 percent for a design speed of 30 mi/h, depending on the type of highway. Table 15.4 gives recommended values of maximum grades. Note that these recommended maximum grades should not be used frequently, particularly when grades are long and the traffic includes a high percentage of trucks. On the other hand, when grade lengths are less than 500 ft and roads are one-way in the downgrade direction, maximum grades may be increased by up to 2 percent, particularly on lowvolume rural highways. Minimum grades depend on the drainage conditions of the highway. Zeropercent grades may be used on uncurbed pavements with adequate cross slopes to laterally drain the surface water. When pavements are curbed, however, a longitudinal grade should be provided to facilitate the longitudinal flow of the surface water. It is customary to use a minimum of 0.5 percent in such cases, although this may be reduced to 0.3 percent on high-type pavement constructed on suitably crowned, firm ground. 15.2 DESIGN OF THE ALIGNMENT The alignment of a highway is composed of vertical and horizontal elements. The vertical alignment includes straight (tangent) highway grades and the parabolic curves that connect these grades. The horizontal alignment includes the straight (tangent) sections of the roadway and the circular curves that connect their change in direction. The design of the alignment depends primarily on the design speed selected for the highway. The least costly alignment is one that takes the form of the natural topography. It is not always possible to select the lowest cost alternative because the designer must adhere to certain standards that may not exist on the natural topography. It is important that the alignment of a given section has consistent standards to avoid sudden changes in the vertical and horizontal layout of the highway. It is also important that both horizontal and vertical alignments be designed to complement each other, since this will result in a safer and more attractive highway. One factor that should be considered to achieve compatibility is the proper balancing of the grades of tangents with curvatures of horizontal curves and the location of horizontal and vertical curves with respect to each other. For example, a design that achieves horizontal curves with large radii at the expense of steep or long grades is a poor design.

Table 15.4 Recommended Maximum Grades Rural Collectors a Design Speed (mi /h) Type of Terrain 20 25 30 35 40 45 50 55 60 Grades (%) Level 7 7 7 7 7 7 6 6 5 Rolling 10 10 9 9 8 8 7 7 6 Mountainous 12 11 10 10 10 10 9 9 8 Urban Collectors a Design Speed (mi /h) Type of Terrain 20 25 30 35 40 45 50 55 60 Grades (%) Level 9 9 9 9 9 8 7 7 6 Rolling 12 12 11 10 10 9 8 8 7 Mountainous 14 13 12 12 12 11 10 10 9 Rural Arterials Design Speed (mi /h) Type of Terrain 40 45 50 55 60 65 70 75 80 Grades (%) Level 5 5 4 4 3 3 3 3 3 Rolling 6 6 5 5 4 4 4 4 4 Mountainous 8 7 7 6 6 5 5 5 5 Rural and Urban Freeways b Design Speed (mi /h) Type of Terrain 50 55 60 65 70 75 80 Grades (%) Level 4 4 3 3 3 3 3 Rolling 5 5 4 4 4 4 4 Mountainous 6 6 6 5 5 Urban Arterials Design Speed (mi /h) Types of Terrain 30 35 40 45 50 55 60 Grades (%) Level 8 7 7 6 6 5 5 Rolling 9 8 8 7 7 6 6 Mountainous 11 10 10 9 9 8 8 a Maximum grades shown for rural and urban conditions of short lengths (less than 500 ft) and on one-way downgrades may be up to 2% steeper. b Grades that are 1% steeper than the value shown may be used for extreme cases in urban areas where development precludes the use of flatter grades and for one-way downgrades, except in mountainous terrain. SOURCE: Adapted from A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D.C., 2004. Used with permission. 755

756 Part 4 Location, Geometrics, and Drainage Similarly, if sharp horizontal curves are placed at or near the top of pronounced crest vertical curves at or near the bottom of a pronounced sag vertical curve, a hazardous condition will be created at these sections of the highway. Thus, it is important that coordination of the vertical and horizontal alignments be considered at the early stages of preliminary design. 15.2.1 Vertical Alignment The vertical alignment of a highway consists of straight sections known as grades, (or tangents) connected by vertical curves. The design of the vertical alignment therefore involves the selection of suitable grades for the tangent sections and the appropriate length of vertical curves. The topography of the area through which the road traverses has a significant impact on the design of the vertical alignment. Vertical curves are used to provide a gradual change from one tangent grade to another so that vehicles may run smoothly as they traverse the highway. These curves are usually parabolic in shape. The expressions developed for minimum lengths of vertical curves are therefore based on the properties of a parabola. Figure 15.11 illustrates vertical curves that are classified as crest or sag. Length of Crest Vertical Curves Provision of a minimum stopping sight distance (SSD) is the only criterion used for design of a crest vertical curve. As illustrated in Figures 15.12 and 15.13, there are PVl A E G 2 G 1 PVC G 1 L 2 TYPE I L PVT G 2 G 1 TYPE II G 2 (a) Crest vertical curves G 1 G 2 G 1 G 2 L 2 L G 2 G 1 TYPE III (b) Sag vertical curves G 1, G 2 = grades of tangents (%) A = algebraic difference L = length of vertical curve PVC = point of vertical curve PVI = point of vertical intersection PVT = point of vertical tangent TYPE IV Figure 15.11 Types of Vertical Curves

Chapter 15 Geometric Design of Highway Facilities 757 P X 1 X 3 = L/2 X 2 G 1 H 1 C PVC L S PVT N H 2 D G 2 L = length of vertical curve (ft) S = sight distance (ft) H 1 = height of eye above roadway surface (ft) H 2 = height of object above roadway surface (ft) G 1, G 2 = grades of tangents (%) PVC = point of vertical curve PVT = point of vertical tangent Figure 15.12 Sight Distance on Crest Vertical Curve (S L) P PVC G 1 H 1 C N S 1 S 2 D S H 2 PVT L G 2 L = length of vertical curve (ft) S = sight distance (ft) H 1 = height of eye above roadway surface (ft) H 2 = height of object above roadway surface (ft) G 1, G 2 = grades of tangents (%) PVC = point of vertical curve PVT = point of vertical tangent Figure 15.13 Sight Distance on Crest Vertical Curve (S L) two possible scenarios that could control the design length: (1) the SSD is greater than the length of the vertical curve, and (2) the SSD is less than the length of the vertical curve. Consider the case when the SSD is greater than the length of the vertical curve as shown in Figure 15.12 where the driver eye height in a vehicle on the grade at point C is H 1 ft. and the object at point D seen by the driver is H 2 ft. The driver s line of sight is PN ft and the SSD is S ft. The line of sight, PN, may not necessarily be horizontal, but the value used in calculations for SSD considers the horizontal projection. From the properties of the parabola, X 3 L 2

758 Part 4 Location, Geometrics, and Drainage The SSD S is S X 1 L 2 X 2 (15.1) X 1 and X 2 can be determined from grades G 1 and G 2 and their algebraic difference A. The minimum length of the vertical curve for the required sight distance is obtained as L min 2S 2001 2H 1 2H 2 2 2 1for S L2 A (15.2) It had been the practice to assume that the height H 1 of the driver is 3.75 ft, and the height of the object is 0.5 ft. Due to the increasing number of compact automobiles on the nation s highways, the height of the driver s eye is now assumed to be 3.5 ft, and the object height, considered to be the tailight of a passenger car, is 2.0 ft. Under these assumptions, Eq. 15.2 can be written as L min 2S 2158 A 1for S L2 (15.3) When the sight distance is less than the length of the crest vertical curve, the configuration shown in Figure 15.13 applies. Similarly, the properties of a parabola can be used to show that the minimum length of the vertical curve is AS 2 L min 1for S L2 2 20012H 1 2H 2 2 (15.4) Substituting 3.5 ft for H 1 and 2.0 ft for H 2, Eq. 15.4 can be written as L min AS2 1for S L2 2158 (15.5) Example 15.1 Minimum Length of a Crest Vertical Curve A crest vertical curve is to be designed to join a 3% grade with a 2% grade at a section of a two-lane highway. Determine the minimum length of the curve if the design speed of the highway is 60 mi/h, S L, and a perception-reaction time of 2.5 sec. The deceleration rate for braking (a) is 11.2 ft /sec 2. Solution: Use the equation derived in Chapter 3 to determine the SSD required for the design conditions. (Since the grade changes constantly on a vertical curve, the worst-case value for G of 3% is used to determine the braking distance.)

Chapter 15 Geometric Design of Highway Facilities 759 SSD 1.47ut 1.47 60 2.5 220.50 377.56 598.1 ft Use Eq. 15.5 to obtain the minimum length of vertical curve: u 2 30 ea a 32.2 b G f L min AS2 2158 5 1598.122 2158 828.8 ft 60 2 30 e 11.2 0.03 f 32.2 Example 15.2 Maximum Safe Speed on a Crest Vertical Curve An existing vertical curve on a highway joins a 4.4% grade with a 4.4% grade. If the length of the curve is 275 ft, what is the maximum safe speed on this curve? What speed should be posted if 5 mph increments are used? Assume a 11.2 ft /sec 2, perception-reaction time 2.5 sec, and that S L. Solution: Determine the SSD using the length of the curve and Eq. 15.5. L min AS2 2158 8.8 S2 275 2158 S 259.69 ft Determine the maximum safe speed for this sight distance using the equation for SSD from Chapter 3. 259.69 1.47 2.5u u 2 30c 11.2 0.044s 32.2

760 Part 4 Location, Geometrics, and Drainage which yields the quadratic equation u 2 33.50u 2367.02 0 Solve the quadratic equation to find the u, the maximum safe speed. u 34.7 mi/h The maximum safe speed for an SSD of 259.69 ft is therefore 34.7 mi/h. If a speed limit is to be posted to satisfy this condition, a conservative value of 30 mi/h will be used. Length of Sag Vertical Curves The selection of the minimum length of a sag vertical curve is controlled by the following four criteria: (1) SSD provided by the headlight, (2) comfort while driving on the curve, (3) general appearance of the curve, and (4) adequate control of drainage at the low point of the curve. Minimum Length based on SSD Criterion. The headlight SSD requirement is based on the fact that sight distance will be restricted during periods of darkness whereas during daylight periods, sight distance is unaffected by the sag curve. As a vehicle is driven on a sag vertical curve at night, the position of the headlight and the direction of the headlight beam will dictate the stretch of highway ahead that is lighted. Therefore the distance that can be seen by the driver is controlled by the headlight beam. Figure 15.14 is a schematic of the case when S L. The headlight is located at a height H above the ground, and the headlight beam is inclined upward at an angle b to the horizontal. The headlight beam intersects the road at point D, thereby restricting the available SSD S. The values used by AASHTO for H and b are 2 ft and 1 degree, respectively. Using the properties of the parabola, it can be shown that 2001H S tan b2 L min 2S 1for S L2 (15.6) A Substituting 2 ft for H and 1 degree for b in Eq. 15.6 yields the following: 1400 3.5S2 L min 2S A 1for S L2 (15.7) Similarly, for the condition when S L, it can be shown that L min AS 2 1for S L2 2001H S tan b2 (15.8) and substituting 2 ft for H and 1 degree for b in Eq. 15.8 yields L min AS 2 1for S L2 400 3.5S (15.9)