9.2 Geometric Design of Highway

9.2 Geometric Design of Highway

Introduction to Geometric Design

Geometric design is the process of defining the physical layout and dimensions of a highway to provide safe, efficient, and comfortable movement of vehicles while being economically feasible to construct. It deals with the three-dimensional alignment—the horizontal curvature, vertical profile, and cross-sectional elements—considering the dynamic characteristics of vehicles, driver psychology, and traffic patterns. Good geometric design minimizes accidents, reduces vehicle operating costs, and enhances the aesthetic value of the roadway.

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1. Basic Design Control and Criteria

Geometric design is governed by a set of fundamental controls and criteria that ensure consistency and safety.

1.1 Design Vehicle

• Definition: A selected motor vehicle used to establish key design controls such as lane width, curve radius, and sight distance.

• Types: Passenger car (most critical for sight distance), bus, truck (single-unit and semi-trailer), and in some cases, agricultural vehicles.

• Key Dimensions: Wheelbase, overall length, width, height, and turning radius govern design elements like intersection corners and parking facilities.

1.2 Design Speed

• Definition: The maximum safe speed that can be maintained over a specified section of highway when conditions (weather, visibility, traffic) are so favorable that the design features of the highway govern. It is the single most critical parameter as it directly influences:

  • Horizontal and vertical curve radii.

  • Superelevation.

  • Sight distances (Stopping, Overtaking).

  • Lane and shoulder width.

• Selection: Based on the functional classification of the road (Artery, District, Village), terrain (flat, rolling, mountainous), and anticipated operating speed. It is not necessarily the legal speed limit.

1.3 Topography (Terrain)

• Classification:

  • Level (Plains): Where highway sight distances are generally long.

  • Rolling: Where natural slopes consistently rise above and fall below the road grade, restricting sight distances.

  • Mountainous: Where longitudinal and transverse changes in elevation are abrupt, necessitating frequent sharp curves and steep grades.

• Impact: Terrain dictates the ruling gradient, curve design, and earthwork quantities. Design speed is lower in hilly and mountainous terrain.

1.4 Traffic Factors

• Design Hourly Volume (DHV): The traffic volume used for design, typically the 30th highest hourly volume of the year. Roads are not designed for the absolute peak but for a volume that is exceeded only 29 times a year.

• Directional Distribution: The split of traffic in each direction (e.g., 60/40 during peak hours).

• Vehicle Mix: Percentage of different vehicle types (cars, trucks, buses, non-motorized). A high proportion of trucks affects climbing lane requirements and sight distance.

1.5 Environmental and Aesthetic Factors

• Design should blend with the natural surroundings, minimize cut-and-fill scars, and preserve scenic views. Social and environmental impact assessments are mandatory.

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2. Elements of Highway Cross-section

The cross-section shows the composition and dimensions of the highway at right angles to the centerline.

1. Right of Way (ROW):

   • The total land area acquired for the highway, including the roadway, slopes, drainage, and future widening.

   • Varies with road class (e.g., 50-60m for Arterial Roads, 20-30m for Village Roads).

2. Roadway (Formation Width):

   • The portion of the ROW within which the road is constructed. It includes the carriageway and shoulders.

3. Carriageway (Pavement):

   • The paved width used for vehicular movement.

   • Lane Width: Standard is 3.5m for single lanes and 3.5-3.75m per lane on multi-lane highways.

   • Number of Lanes: Determined by traffic volume and level of service.

4. Shoulders:

   • Paved or unpaved strips adjacent to the carriageway.

   • Functions: Provide lateral support to the pavement, emergency stopping space, space for disabled vehicles, and recovery area for errant vehicles.

   • Width: Typically 2.5m for paved shoulders on major highways, minimum 1.5m for earthen shoulders.

5. Side Slopes and Berms:

   • Cut Slope: Slope of the excavation (e.g., 1:1 to 1:1.5 in soil, steeper in rock).

   • Fill Slope (Batter): Slope of the embankment (e.g., 1:1.5 to 1:2).

   • Berm (Ditch): A drainage channel located between the toe of the fill slope or edge of cut and the ROW boundary.

6. Medians (Dividers):

   • Used on multi-lane highways to separate opposing traffic flows.

   • Functions: Prevent head-on collisions, provide space for future lanes, reduce headlight glare, and act as a refuge for pedestrians.

   • Types: Raised (paved), depressed (grassed), or barrier-type.

7. Sidewalks/Footpaths:

   • Provided in urban areas and villages for pedestrian safety.

8. Drainage Channels:

   • Side Drains (Kerb and Gutter in urban areas): Collect surface runoff from the roadway and adjacent land.

   • Cross-Drainage Structures: Culverts and bridges to channel water across the road.

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3. Highway Curves and Superelevation

3.1 Horizontal Curves

• Purpose: To change the direction of the highway alignment.

• Types:

  1. Simple Curve: A circular arc of constant radius connecting two tangents.

  2. Compound Curve: Two or more simple curves with different radii turning in the same direction.

  3. Reverse Curve: Two simple curves turning in opposite directions (requires a tangent or transition curve in between for safety).

  4. Transition Curve: A curve with a gradually changing radius (spiral or lemniscate) inserted between a tangent and a circular curve or between two circular curves.

3.2 Superelevation (Banking)

1. Purpose: To counteract the centrifugal force developed when a vehicle travels on a horizontal curve, thereby reducing the tendency to skid or overturn and providing rider comfort.

2. Definition: The transverse slope provided across the carriageway, raising the outer edge with respect to the inner edge.

3. Formula: The equilibrium equation for a vehicle on a banked curve (ignoring friction) is: $e + f = \frac{V^2}{127 R}$ Where:

   • $e$ = Superelevation rate (expressed as a decimal, e.g., 0.07 for 7%).

   • $f$ = Lateral friction factor (coefficient of friction between tire and pavement, typically 0.15).

   • $V$ = Design speed in km/h.

   • $R$ = Radius of the horizontal curve in meters.

4. Maximum Superelevation: Limited for safety in slow-moving traffic or icy conditions. In Nepal's Road Standards 2070, maximum $e_{max}$ = 0.07 (7%) for plain/rolling terrain and 0.10 (10%) for mountainous terrain.

5. Attainment of Superelevation:

   • Method: Rotating the pavement cross-section about the inner edge, centerline, or outer edge.

   • Runoff Length: The length over which the full superelevation is developed, typically provided within the transition curve length.

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4. Average and Ruling Gradients

4.1 Gradient

• Definition: The rate of rise or fall of the road surface along its alignment. Expressed as a percentage (%) or ratio (e.g., 1 in n).

4.2 Types of Gradients

1. Ruling Gradient:

   • The maximum gradient that is commonly adopted in a particular section of the road under normal conditions.

   • It determines the sustainable speed of loaded trucks without an unacceptable drop in speed. Example: 1 in 30 (3.33%) in plains, 1 in 20 (5%) in hills.

2. Limiting Gradient:

   • Steeper than the ruling gradient.

   • Used where adopting the ruling gradient would lead to excessive earthwork (deep cuttings or high embankments) and significantly higher cost.

   • Its length is restricted. Example: 1 in 16.7 (6%) in hills.

3. Exceptional Gradient:

   • Steeper than the limiting gradient.

   • Used only in extremely difficult terrain for very short stretches (not more than 100m at a stretch).

   • Requires special justification and design.

4. Average Gradient:

   • The total rise or fall over a significant length of road (e.g., 1 km) divided by its horizontal length.

   • Provides an overall measure of the steepness of a road section. The ruling/limiting gradients control the design at every point.

4.3 Importance

• Steep gradients increase fuel consumption, reduce vehicle speed (especially for trucks), necessitate more powerful engines, and can be unsafe on downhill sections due to brake failure.

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5. Stopping Sight Distance (SSD)

5.1 Definition

• The minimum sight distance available on a highway at any spot, sufficient to enable a driver traveling at the design speed to stop his vehicle safely before colliding with a stationary object on the road.

5.2 Components of SSD

SSD is the sum of two distances:

1. Lag Distance (Distance traveled during Perception-Reaction Time):

   • The distance the vehicle travels during the driver's total reaction time ($t$).

   • $d_1 = 0.278 V t$, where $V$ is in km/h, $t$ is in seconds (standard $t$ = 2.5 sec).

2. Braking Distance:

   • The distance traveled by the vehicle after the brakes are applied until it comes to a complete stop.

   • $d_2 = \frac{V^2}{254 f}$

   • $f$ = longitudinal coefficient of friction between tire and road (depends on speed and surface condition).

5.3 Formula

$SSD = d_1 + d_2 = 0.278 V t + \frac{V^2}{254 f}$

5.4 Importance

• Absolute Minimum Requirement: SSD must be available at every point on the road.

• Critical Design Application: Governs the design of:

  • Vertical Curves (Crest/Sag): Length of summit curves is designed based on SSD.

  • Horizontal Curves: Sight distance around curves must be > SSD. This may require clearing obstructions (Setback Distance).

  • Intersection Design: Sight triangles at intersections must provide SSD.

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6. Design Considerations for Specific Elements

6.1 Horizontal Alignment Design

• Objective: To achieve smooth, safe, and comfortable transition between straight sections.

• Key Principles:

  1. Use gentle curves with large radii wherever possible.

  2. Avoid sudden changes from long tangents to sharp curves.

  3. Use transition curves between tangents and circular curves.

  4. Avoid compound and reverse curves on high-speed roads unless absolutely necessary.

  5. Ensure that the sight distance around the curve is adequate (check for obstructions like cut slopes or buildings).

6.2 Vertical Alignment Design

• Objective: To provide a smooth grade line with gradual changes consistent with the topography, drainage, and safety.

• Key Principles:

  1. Vertical Curves: Parabolic curves are used for smooth transition between grade lines.

     • Summit (Crest) Curves: Convex. Designed for Stopping Sight Distance (SSD).

     • Valley (Sag) Curves: Concave. Designed for headlight sight distance (at night) and rider comfort (centrifugal force).

  2. Length of Vertical Curve (L): For a given algebraic difference in grades ($A$), $L$ is calculated based on SSD.

     • When $L > SSD$: $L = \frac{A S^2}{100(\sqrt{2h_1} + \sqrt{2h_2})^2}$ (for summit, where $h_1$=driver eye height, $h_2$=object height).

     • When $L < SSD$: $L = 2S - \frac{200(\sqrt{h_1} + \sqrt{h_2})^2}{A}$.

  3. Provide adequate drainage by maintaining a minimum gradient (e.g., 0.5%) in flat areas.

6.3 Extra Widening on Curves

1. Need: On horizontal curves, the tracking width of a vehicle increases due to:

   • Mechanical Widening: The rear wheels track inside the front wheels (off-tracking).

   • Psychological Widening: Drivers tend to keep a greater clearance from the edge and oncoming vehicles on curves.

2. Formula (for single lane): $W_e = \frac{l^2}{2R} + \frac{V}{9.5\sqrt{R}}$ Where $W_e$ = extra widening (m), $l$ = wheelbase of design vehicle (m), $V$ = speed (km/h), $R$ = curve radius (m).

3. Provision: Added to the inner side of the curve, typically distributed 2/3 on the inner side and 1/3 on the outer side for multi-lane roads.

6.4 Setback Distance (Clearance to Sight Obstruction)

1. Definition: The distance required from the centerline of the inside lane of a horizontal curve to any sight obstruction (like a building, cut slope, or dense vegetation) to ensure the required Stopping Sight Distance is available around the curve.

2. Purpose: To define the "clear zone" on the inside of a curve that must be kept free of obstructions.

3. Calculation: Depends on the curve radius ($R$), SSD ($S$), and the distance from the obstruction to the centerline ($m$). For simple circular curves, the relationship is approximated by: $m = R \left( 1 - \cos \frac{28.65 S}{R} \right)$ (Where $S$ and $R$ are in meters, and the angle is in degrees). Design manuals provide graphical solutions or tables.

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7. Design of Road Drainage Structures

Effective drainage is crucial for road longevity and safety. It involves removing surface and subsurface water from the roadway.

7.1 Surface Drainage

• Objective: To intercept and remove surface runoff from the carriageway and adjacent land before it can infiltrate or cause erosion.

• Components:

  1. Cross Slope (Camber): Transverse slope of the carriageway (2-3%) to shed water to the sides.

  2. Side Drains (Kerb and Gutter in urban areas): Channels along the road to collect and convey water.

  3. Catch Basins and Inlets: Openings to collect water from the road surface into underground drains.

  4. Cross-Drainage Structures:

     • Culverts: Small bridges (typically < 6m span) for water to pass under the road. Types: Pipe, Box, Arch.

     • Bridges: For larger water crossings (> 6m span).

     • Causeys/Vents: Openings in low embankments.

7.2 Subsurface Drainage

• Objective: To lower the water table and intercept seepage water to prevent subgrade weakening and pavement failure.

• Components: Subsurface drains (perforated pipes), blanket drains, and interceptor drains.

7.3 Hydrological Design

• Involves calculating the peak runoff discharge (Q) for a given catchment area using methods like the Rational Formula: $Q = \frac{1}{36} C i A$ (Where $C$ = runoff coefficient, $i$ = rainfall intensity in mm/hr, $A$ = catchment area in hectares).

• Culvert size and bridge waterway are designed to safely pass this peak flow with a specific return period (e.g., 25-year flood for major highways).

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8. Design Considerations for Hill Roads

Designing roads in hilly and mountainous terrain presents unique challenges.

8.1 Alignment

• Dominant Control: Gradient is the primary constraint. Alignments often follow natural contours.

• Types of Hill Road Alignment:

  1. Contour Road/Ridge Line: Follows a contour, gentle gradient, but long length.

  2. Valley Line: Follows a stream, good drainage but flood risk.

  3. Side Hill Line: Compromise between contour and valley lines.

  4. Staircase/Switchback Line: Used on steep hillsides, involves zigzags with hairpin bends.

8.2 Geometric Standards

• Design Speed: Lower (e.g., 30-60 km/h).

• Gradients: Ruling (5-6%), Limiting (6-7%), Exceptional (up to 10% for short stretches).

• Curves: Minimum radius is small, necessitating careful superelevation design (up to 10% allowed).

• Sight Distance: Often restricted. Requires frequent provision of passing bays on single-lane roads.

8.3 Hairpin Bends

• Definition: Very sharp reverse curves (often 180°) used to gain elevation in a confined space.

• Design Elements: Large curve radius (as large as site permits), adequate transition, superelevation, and extra widening.

8.4 Slope Stability and Protection Works

• Cut Slopes: Must be properly designed (slope angle, benching) and protected from erosion and rockfalls using retaining walls, breast walls, drip courses, and drapery systems.

• Fill Slopes: Require proper compaction and toe protection. Retaining walls are used where space is limited.

8.5 Drainage in Hill Roads

• Critical Importance: Water is the main cause of slope failures.

• Special Features:

  • Catch Water Drains: At the top of cuts to intercept surface runoff.

  • Side Drains with Lining: To prevent scour.

  • Cross-Drainage: Frequent culverts to prevent water concentration.

8.6 Landslide Mitigation

• Design must identify and avoid unstable zones. If unavoidable, require specialized treatments like soil nailing, anchoring, and extensive subsurface drainage.

Conclusion: Geometric design synthesizes engineering principles with human factors and environmental constraints. A well-designed highway is not just a path for vehicles but a system that promotes safety, efficiency, economy, and harmony with its surroundings, whether in the plains or the challenging Himalayas.