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Horizontal Transition Curves for Highways and Its Calculation

What is transition curve and when it is needed?

Transition curve is a curve in plan which is provided to change the horizontal alignment from straight to circular curve gradually means the radius of transition curve varies between infinity to R or R to infinity.

Objectives for providing transition curves

1. For the gradual introduction Centrifugal force
2. To introduce super elevation gradually
3. To introduce extra widening gradually
4. To provide comfort for the driver that is to enable smooth vehicle operation on road.
5. To enhance aesthetics of highways.

Types of transition curves

• Spiral or clothoid
• Cubic parabola
• Lemniscate

IRC recommends Spiral or clothoid as the ideal transition curve due to following reasons:

1. It satisfies that rate of change of centrifugal acceleration is constant i.e., Ls.R = constant. Where Ls = length of transition curve R = radius of curve.
2. The calculation and field implementation of spiral curve is simple and easy.
3. It enhances aesthetics also.

Determining length of transition curve

The length of transition curve can be calculated by 3 conditions.

• Based on rate of change of acceleration
• Based on rate of change of super elevation and extra widening
• Based in IRC empirical formula

Based on rate of change of acceleration

Radius of curve is infinity at the tangent point and hence centrifugal acceleration is zero. Similarly at the straight end radius of curve has minimum value means centrifugal acceleration is maximum. So, the rate of change of centrifugal acceleration should be adopted such that the design should not cause any discomfort to the drivers.

Let Ls be the length of transition curve and a vehicle is moving with a speed of V m/s.

Force P = (mV2/R)

Since it is similar to F= ma

P = m (V2/R)

Therefore, centrifugal acceleration = V2/R

Let “C” be the coefficient of rate of change of centrifugal acceleration.

C = (V2/R). (1/t)

Where t= time taken to travel the transition curve of length Ls, with a speed of V

t = Ls/V

C = (V2/R). (V/Ls)

Ls = (V3/CR)

According to IRC, C = 80/(75+V) and C should be (0.5<C<0.8).

Based on rate of change of superelevation and extra widening

Let 1 in N is the allowable rate of introduction of super elevation and E is the raise of the outer edge with respect to inner edge. W is the normal width of pavement in meters. We is the extra width of pavement in meters. And e is the rate of superelevation.

E = (W+We).e

Therefore length of transition curve, Ls = (W+We).e.N

If the pavement outer edge is raised and inner edge is depressed with respect to center of pavement then,

Ls = [(W+We).e.N]/2

Typical range of introduction of super elevation is as follows according to IRC

Type of terrain	Rate of super elevation 1 in N
For plain and rolling terrains	1 in 150
For built up areas	1 in 100
For hilly and steep terrains	1 in 60

Based on IRC empirical formula

IRC given some direct formulae for finding the length of transition curve.

• For plain and ruling terrain:

Ls = 2.7 (V2/R)

• For mountainous and steep terrains

Ls = V2/R

Hence these are the three criteria to determine the length of transition curve. The maximum of above three conditions will be considered as the length of transition curve.

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

  

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Air-Entrained Cement – Manufacture, Properties and Advantages

Air-entrained portland cement is a special cement which has air bubbles introduced in the cement or concrete that provides the space for expansion of minute droplets of waters in the concrete due to freezing and thawing and protects from cracks and damage of concrete.

In this article we discuss about manufacture, air entraining agents, properties, advantages and disadvantages.

Manufacture of Air-Entrained Cement

The manufacture of this special concrete is same as that of normal ordinary portland cement, after the cement clinkers are formed, in the grinding process the cement clinkers are added with some air entraining materials which makes the cement as air entrained cement.

The ways of incorporating air in concrete:

1. Using gas forming materials as aluminium powder, zinc powder and hydrogen peroxide.
2. Using surface active agents that reduces surface tension. They may be natural wood resins and their soaps, animal or vegetable fats or oils, alkali salts of sulfonated or sulphated organic compounds.
3. Using cement dispersing agents.
4. Calcium ligno-sulphate and Calcium salts of glues.

Fig 1: Process of expansion of water droplets in concrete.

Properties of Air-Entrained Cement

The following are properties of air entrained concrete:

1. Workability

The workability property of this cement is high due to the air bubbles which act as lubricant between aggregates, which reduces water and sand requirement and hence increases strength of the concrete. It else reduce segregation and bleeding of plastic concrete.

2. Strength

Abraham’s law is well know for a civil engineer. Strength and the W/C ratios are inversely proportional to each other. Less the W/C ratio, greater is the strength. With the use of air entrainer , the W/C ratio is kept low and hence the strength parameter of the concrete is not compromised.

But it is difficult to attain high level strength concrete with air-entrained cement.

3. Freezing and Thawing Durability

In the cold environment, due to low temperature the water inside the concrete freezed and expands. Use of this cement provides required space for the water to expand and thus doesn’t let the concrete to rupture. However, entrained air bubbles serve as reservoirs for the expanded water, thereby relieving expansion pressure and preventing concrete damage.

4. Sulphate Resistance 

The resistance ability for sulphate attack is high in the air entrained cement as the W/c ratio can be kept low, which initiates the sulphate attack.

5. Permeability

The permeability of air entrained concrete is greater than that of non air-entrained concrete as the air bubbles break the capillary channels. Therefore, use air-entrained concrete where water tightness is a requirement.

6. De-Icing Resistance

In the sloped structure, the ice is formed on the building. To remove these ice, de-icing chemicals used for snow and ice removal. The use of this chemicals forms a layer of scales in the concrete. Air entrained cement prevents scaling caused by de-icing chemicals and is recommended for all applications where the concrete contacts de-icing chemicals.

Fig 2: Bubbles formation in concrete due to air entained cement.

Advantages of Air-Entrained Cement

The advantages of air entrained concrete are,

1. Workability of concrete increases.
2. Use of air entraining agent reduces the effect of freezing and thawing.
3. Bleeding, segregation and laitance in concrete reduces.
4. Entrained air improves the sulphate resisting capacity of concrete.
5. Reduces the possibility of shrinkage and crack formation in the concrete surface.

Disadvantages of Air-Entrained Cement

The disadvantages of air entrained concrete,

1. The strength of concrete decreases.
2. The use of air entraining agent increases the porosity of concrete thereby reducing the unit weight.
3. Air-entrainment in concrete must not be done if the site control is not good. This is due to the fact that the air entrained in a concrete varies with the change in sand grading, errors in proportioning and workability of the mix and temperatures.

  

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Hydrophobic Cement – Manufacture, Properties and Uses

As the name of the cement denotes, hydro means water and phobic means against. Hydrophobic cement is obtained by grinding portland cement clinker with a film-forming substance such as oleic acid in order to reduce the rate of deterioration when the cement is stored under unfavourable conditions. It is also known as Hydrographic cement.

In this article we discuss about the manufacture, properties, uses, advantages, disadvantages and safety precautions of hydrophobic cement.

Fig 1: Water resistant concrete made of Hydrophobic cement.

Manufacture of Hydrophobic Cement

The process of manufacture of this special cement is same as that of portland cement. The clinkers formed in the manufacture of cement are grinded with water repellent film substance such as Oleic Acid or Stearic Acid. These chemicals form a layer on the cement particle and does not allow water to mix and start hydration process in the transportation or storage stage. Anyhow during the mixing process, due to great agitation, this layer of water repellent break and allows the hydration to take place.

Properties of Hydrophobic Cement

Table 1: Properties and their values of Hydrophobic cement.

Properties	Value
Fineness	350 m2/kg
Soundness
Lechatelier (mm)	10mm
Autoclave	0.8 %
Setting Time
Initial Setting	30min
Final Setting	600min
Compressive Strength
3days	16 MPa
7days	22 MPa
28days	30 MPa
Water Absorption	0.3 – 1 %

Uses of Hydrophobic Cement

1. Uses in longer storage periods and extremely wet climatic conditions.
2. Majorly used in the Tunnel construction as the underground repairs are difficult and costly.
3. These cements are used in construction of dams, spillways, under water constructions.
4. Used in the structures that are exposed to rain or rain puddling, such as green roofs, other kinds of roofs, parking structures, and plazas.
5. Used in drainage system works and manholes.
6. Used in water treatment plants , dams and retaining walls.
7. It can fix leaky pipes and basements without having to stop the leaking.

Advantages of Hydrophobic Cement

The major advantages of hydrophobic cement are,

1. Provide durable repairs that will last for long period of times.
2. Strength is same as that of ordinary cement.
3. Sets and hardens fast, normally three minutes after being mixed with water.
4. Setting time is fast, hardens fast, thus it can be painted within one hour of it being applied.

Disadvantages of Hydrophobic Cement

The major disadvantages of hydrophobic cement are,

1. Does not work on frozen surfaces.
2. Cannot be used when the temperature is below 40 degrees Fahrenheit.
3. This cement solves the problem of leaking, but does not solve the problems which are due to condensation.
4. Needs skilled labour and favourable climatic conditions to use this type of cement.
5. Cost is high as it is very expensive.

Health and Safety Precautions of Hydrophobic Cement

1. Avoid breathing the dust.
2. Avoid any contact with eyes or skin.
3. Silica inhaling may cause lung problems, although there is no real evidence silica is a carcinogen.
4. The use of protective clothing: gloves or mask is recommended.