Vertical alignment
7.6 GraDELINE DEVELOPMENt
The longitudinal section contains virtually all the information necessary to build the road. At the top of the sheet, the profile is presented. This includes the ground line, typically under the centreline of the road, and the gradeline. Because of its application in the development of the mass-haul curve, the gradeline represents the top of the earthworks, hence, as previously stated, often referred to as the subgrade. The data defining the vertical curves are normally shown on the profile. These data are
• The heights of the VPIs • The length of curves
• The entry and exit gradients • The K-value of the curves
The longitudinal section is drawn to a distorted scale, usually of 10V:1H. As gradients are very low, typically 6 per cent or less, it is very difficult to create a mental picture of the gradeline without this distortion. While drawing the gradeline is usually by the use of soft- ware, it is useful to have some idea of the mechanics of drawing it manually.
Plastic templates of different radii, known as ship or railway curves, are used to construct the vertical curves. These templates are, in fact, circular but, because of the distortion, are a reasonable approximation of the parabola.
As a rule of thumb, the radius of the railway curve in centimetres is equal to the K-value of the vertical curve when the distortion is 1:10. This applies to the middle third of the curve. The outside thirds can be approximated by using a longer radius railway curve between the plotted position of the BVC or EVC and the already drawn section of the curve. The outside curves can have anything up to double the radius of the inner curve.
It sometimes happens that the curve being drawn is so long that it cannot be drawn with a single template. A useful device then is to draw a line between the midpoints of the tangents connecting the BVC and EVC to the PI. The vertical curve falls on the midpoint of this line, which is also tangential to the curve. The process can be repeated by a series of halving of the tangent lengths and joining these midpoints. The curve will be tangential to the joining line at the midpoints of these lines.
An extract of the survey plan is typically shown below the longitudinal section as a strip plan. Data defining the horizontal alignment are shown on this survey plan. If space per- mits, the mass-haul diagram is shown below the survey plan.
At the bottom of the sheet, a table is provided containing the following data: • The ground levels
• The gradeline levels
• The bearing of tangents and data defining the horizontal curvature • The superelevation and location of the superelevation development • The location and sizes of culverts
• The location of guardrails, barrier lines and so forth
These data are plotted against a baseline of increasing stake value.
1. The first step in the development of the gradeline is to add all the known information to the drawing, which consists of
• Ground line and the associated levels added to the table • Survey plan
140 Geometric design of roads handbook
• Horizontal alignment data
• The location and height of the control points with the height of the control points also being listed in the table
2. The next step is selection of the grading point. This is the point on the cross-section, through which the gradeline passes. In the case of a two-lane road, the grading point usually is at the theoretical intersection point of the two slopes comprising the camber of the road. It is also the point around which the superelevation is developed.
On dual-carriageway roads, the grading point can either be on the centreline of the cross-section or there may be two grading points with these located at the inner edge of the inside shoulder. This would support the development of split grading between the two carriageways. These grading points could be used in the case also of stage construction of a dual carriageway. In the case of there being two grading points, the ground line is that lying under the centreline of the road.
3. Prepare a trial gradeline, taking into account the vertical controls including culverts, and include coordination of horizontal and vertical alignments as far as practicable. 4. Calculate earthworks quantities and develop a mass-haul diagram.
5. Adjust the vertical alignment so that • All mandatory controls are met
• Discretionary controls are met as far as possible
• Other controlling criteria are satisfied with special consideration given to the loca- tion of intersections and points of access to ensure that minimum sight distances and critical crossfall controls are met
• Earthworks are minimized
Where minimum standards cannot be achieved and compromises have to be made, the designer requires a broad understanding of basic theory and the assumptions made in the development of the standards. All design exceptions should be documented in terms of the process of design exceptions, variances and waivers discussed in Chapter 4.
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Chapter 8
Cross-section design
CONtENtS 8.1 Introduction ... 142 8.2 Basic lanes ... 143 8.3 Auxiliary lanes ... 145 8.3.1 Introduction ... 145 8.3.2 Climbing lanes ... 145 8.3.3 Passing lanes ... 147 8.3.4 Turning lanes ... 150 8.3.5 Additional lanes between intersections ... 150 8.3.6 Additional lanes between interchanges ... 151 8.3.7 Camber and crossfall on the travelled way... 152 8.4 Shoulders ... 152 8.5 Medians ... 155 8.5.1 Introduction ... 155 8.5.2 The function of median islands ... 155 8.5.3 Two-way left-turn lanes ... 156 8.5.4 Median profile ... 156 8.5.5 Median widths ... 157 8.5.6 Median barriers ... 158 8.5.7 Median end treatments and openings ... 159 8.6 Outer separators ... 160 8.7 Boulevards ... 161 8.8 Side slopes ... 162 8.8.1 Slope stability ... 162 8.8.2 Safety ... 163 8.8.3 Aesthetics ... 163 8.9 Verges ... 163 8.9.1 Introduction ... 163 8.9.2 Drainage elements ... 164 8.9.3 Provision for utilities ... 167 8.10 Roadside amenities ... 169 8.10.1 Introduction ... 169 8.10.2 Rest areas ... 169142 Geometric design of roads handbook
8.1 INtrODUCtION
AASHTO (2011a) defines the cross-section as ‘A vertical section of the ground and roadway at right angles to the centreline of the roadway, including all elements of a highway or street from right-of-way line to right-of-way line’. Although many designers are happy to spend considerable periods of time on the horizontal and vertical alignments, the cross-section seems to be in the nature of an afterthought. Other than to accept whatever cross-section the road agency deems to be appropriate for the project, it seems to command little atten- tion or thought. And yet this Cinderella is used to define the very nature of the road being designed. The two-lane two-way road, the 2 + 1, the six-lane dual-carriageway are nothing more or less than names describing the cross-sections of these roads.
Another feature of the cross-section is that, while the horizontal and vertical alignments require considerable calculation, the design of the cross-section is essentially a process of selection and engineering judgment. A belief common to all property developers and, in fact, shared also with many town planners, is that the cross-section is whole and indivisible and spans the full width of the road reserve (in American nomenclature the right-of-way). In fact, it comprises many discrete components, each with its own functions, location within the road reserve and dimensions. The design of the cross-section is thus a process of selec- tion of the components required followed by their sizing.
The components which appear in a cross-section include • The lanes
• Basic • Auxiliary
• Shoulders and sidewalks • Medians
• Outer separators • Boulevards • Cut and fill slopes • Verges
• Drainage elements • Provision for utilities
• Roadside amenities, including • Rest areas
• Trading areas • Traveller facilities
Not all of these components appear in every cross-section. The designer is required to determine precisely what function the road is intended to serve and then to select the com- ponents appropriate to that function. The next step is concerned with locating these compo- nents in the road reserve and, finally, sizing the selected components to properly give effect to their individual functions.
These components are discussed in the following sections of this chapter. 8.10.3 Service stations and restaurants ... 171 8.10.4 Trading areas ... 171 8.11 Road narrowing ... 172 8.12 Vertical and horizontal clearances ... 174 8.13 Typical cross-sections ... 175
Cross-section design 143