What is Vertical Alignment of Highways? Gradients and Vertical Curves

What is vertical alignment of highways?

The vertical alignment of highway generally defined as the presence of heights and depths in vertical axis with respect to horizontal axis of alignment. These heights and depths in roads may be in the form of gradients (straight lines in a vertical plane) or vertical curves.

Vertical alignment of highways consists of

• Gradients
• Grade compensation
• Vertical curves (valley curve, summit curve)

Gradients

Gradient is defined as the rise or fall corresponding to some horizontal distance.

Raise with respect to horizontal distance is called Upward gradient (+n %)

Fall with respect to Horizontal distance is called Downward Gradient (-n %)

Gradient is represented as below fig:

Types of gradients

• Ruling gradient
• Limiting gradient
• Exceptional gradient
• Minimum gradient

Ruling gradient

This is the maximum gradient which is generally used to design the vertical profile of highway. So it is also called as designer gradient. Ruling gradient depends on the terrain, length of the grade, speed, pulling power of the vehicle and the presence of the horizontal curve. It is adopted by considering a particular speed as the design speed and for a design vehicle with standard dimensions. In flat terrains it is possible to provide flat gradients and in hilly terrains it is very costly and sometimes it is difficult to provide ruling gradient in hilly terrains.

Limiting gradient

This gradient is provided as shorter stretches in highways. Whenever ruling gradients costs high for the hilly terrains then limiting gradient is provided which will reduce the cost. This gradient is adopted frequently in terrains with limited stretches.

Exceptional gradient

These are very steeper gradients given at unavoidable situations and they are adopted for stretches not exceeding 100m of length.

Minimum gradient

To drain of rain water from the road minimum gradient is needed. Generally for lateral drainage Camber is provided. But for the longitudinal drainage along the side drains require some slope for smooth flow of water. For concrete drains minimum gradient of 1 in 500 and open soil drains gradient of 1 in 200 is suitable.

Grade Compensation

When a horizontal circular curve lies in vertical curve there will be an increased resistance offered by the circular curve in the form of curve resistance in addition to the component of gravity.

IRC specifications for grade compensations are as follows.

• For grades flatter than 4% grade compensation is not required due to negligible loss of tractive force.
• Grade compensation is
• Maximum value of gradient compensation =%, R= radius of horizontal curve.

Vertical Curves

Generally two types of vertical curves are there to adopt for the vertical alignment. They are

• Summit curve
• Valley curve

Summit curve

Summit curve is a vertical curve adopted mainly when the gradient is upwards. In case of summit curve simple parabola is considered as best curve shape. There are four different cases are involved in adoption of summit curve as follows.

Case-1:

When upward gradient meets a flat gradient.

Case-2:

When upward gradient meets another upward gradient

Case-3:

When upward gradient meets downward gradient

Case-4:

When downward gradient meets another downward gradient

Valley curve

It is a vertical curve provided when the gradient is downwards. Generally when the vehicle meets downward gradient it accelerates more and discomfort arises. So, in the design of valley curve in vertical alignment comfort is considered along with sight distance. Here also four cases are considered but case 2 and case 3 are same as summit curve and the other cases are as follows.

Case-1:

When downward gradient meets flat gradient

Case-2:

When downward gradient meets upward gradient