Geometric Design II

Gradient

1. Gradient is the rate of rise or fall along the length of the road with respect to the horizontal. While aligning a highway, the gradient is decided for designing the vertical curve. The positive gradient or the ascending gradient is denoted as +n and the negative gradient as −n. 

2. The deviation angle N is: when two grades meet, the angle which measures the change of direction and is given by the algebraic difference between the two grades (n1 − (−n2)) = n1 + n2 = α1 + α2.

Types of Gradients

i) Ruling gradient

ii) Limiting gradient

iii) Exceptional gradient 

iv) Minimum gradient 

• Ruling Gradient

1. The ruling gradient or the design gradient is the maximum gradient with which the designer attempts to design the vertical profile of the road. 

2. This depends on the terrain, length of the grade, speed, pulling power of the vehicle and the presence of the horizontal curve. In flatter terrain, it may be possible to provide flat gradients, but in hilly terrain it is not economical and sometimes not possible also. 

3. The ruling gradient is adopted by the designer by considering a particular speed as the design speed and for a design vehicle with standard dimensions. 

4. But our country has heterogeneous traffic and hence it is not possible to lay down precise standards for the country as a whole. Hence IRC has recommended some values for ruling gradients for different types of terrain. 

• Limiting gradient

1. This gradient is adopted when the ruling gradient results in enormous increase in cost of construction. On rolling terrain and hilly terrain it may be frequently necessary to adopt a limiting gradient. 

2. But the length of the limiting gradient stretches should be limited and must be sandwiched by either straight roads or easier grades.

• Exceptional gradient

Exceptional gradients are very steeper gradients given at unavoidable situations. They should be limited for short stretches not exceeding about 100 meters at a stretch. In mountainous and steep terrain, successive exceptional gradients must be separated by a minimum 100 meter length gentler gradient.

At hairpin bends, the gradient is restricted to 2.5%. Critical length of the grade The maximum length of the ascending gradient which a loaded truck can operate without undue reduction in speed is called critical length of the grade. A speed of 25 kmph is a reasonable value. This value depends on the size, power, load, grad-ability of the truck, initial speed, final desirable minimum speed etc. 

• Minimum gradient

This is important only at locations where surface drainage is important. Camber will take care of the lateral drainage. But the longitudinal drainage along the side drains require some slope for smooth flow of water. Therefore minimum gradient is provided for drainage purposes and it depends on the rain fall, type of soil and other site conditions. A minimum of 1 in 500 may be sufficient for concrete drain and 1 in 200 for open soil drains are found to give satisfactory performance.