Wednesday, September 11, 2013

Road Materials - Soil as Sub-grade

Road Materials are the materials which are used for the construction of the roads, commonly used road materials are, soil, Aggregates and binders.
Soil is used for the construction of the bottom most layer of the pavement, i.e. sub-grade. Here is a short details of the sub-grade and its function.:
Soil as sub-grade material

  • sub-grade is the layer of the pavement whose main function is to support the upper layers of the pavement and to provide the good drainage facility to the infiltrating rain water. It has to act as a single structure along with other layers of the pavement.
  • Soil is compacted to its maximum dry density which can be achieved by using the optimum moisture content and the methods of compaction control. Strength has to be ensured which is required for the given design thickness of the pavement.
  • Strength analysis and the thickness of pavement are inter linked because more thickness of the pavement is needed if the soil is weak but if the soil possess a good strength then less thickness is needed.

This is ensured by using the CBR(California Bearing Ratio) Test which is produced or was first used by the California State Highway Department. Using the CBR test and the empirical charts you can find out the thickness of the flexible pavement required above the sub-grade.

Thanks for your visit!

P.S. for more about the functions of the various pavement layers please visit this article:  Functions of various pavement layers.

Tuesday, September 10, 2013

Westergaard's theory for rigid pavements


Rigid Pavements are constructed with some rigid materials like Cement Concrete(Plain, reinforced or prestressed).

Here the load is transferred  through the slab action not like in the flexible pavements. Westergaard's theory is considered good to design the rigid pavements.

He considered rigid pavement slab as a thin elastic plate resting on soil sub-grade, which is assumed to be a dense liquid. So, here the upward reaction is assumed to be proportional to the deflection, i.e. p = K.d, where K is a constant defined as modulus of subgrade reaction. Units of K are kg/cm^3.

  • Westergaard's modulus of sub-grade reaction:

Modulus of sub-grade reaction is proportional to amount of deflection d. Displacement level is taken as 0.125 cm in calculating K i.e. d = 0.125 cm, so modulus of sub-grade reaction
K = p/d = p/0.125 kg/cm^2

  • Radius of relative stiffness of slab to sub-grade:

Amount of deflection which will occur on the pavement surface depends on the stiffness of the slab and also on the stiffness of the sub-grade. Same amount of deflection will occur on the top surface of the sub-grade.

This means that the amount of deflection which is going to occur in the rigid pavement pavement layer depends both on relative stiffness of the pavement slab with respect to that of sub-grade.

Westergaard defined this by a term "Radius of relative stiffness" which, can be written numerically as below:
            l = [Eh^3/ (12K(1-U^2)]^(1/4)

Where,  l = radius of relative stiffness, cm
         E = Modulus of elasticity of cement concrete kg/cm^2
         U = Poisson's ratio for concrete = 0.15
         K = Modulus of Sub-grade reaction in kg/cm^2

Traffic Parameters:
(1) Design Wheel Load
(2) Traffic Intensity

  • Critical Load Positions:
    Rigid Pavement - a 3D view

When the wheel load is applied on the pavement surface, flexural stresses are induced in the pavement. There are three critical positions which are to be checked for maximum stresses.

  1. Interior loading
  2. Edge Loading
  3. Corner loading
Whenever loading is applied at the interior of the slab, remote than the edges and corner, this is called interior loading.
When loading is applied on the edges, remote than the corners is called edge loading.
When the loading is applied on the corner angle bisector and loading is touching the corner the edges.

  • Equivalent Radius of Resisting section:
When the loading is at the interiors there is a particular area which will resist the bending moment. Westergaard assumed that the area will be circular in plan and its radius is called as Equivalent radius of Resisting section.
     b= (1.6.a^2 + h^2)^(1/2)  - 0.675.h
      b = equivalent radius of resisting section, cm when 'a' is less than 1.724.h
      a = radios of wheel load distribution, cm
      h = slab thickness, cm
When 'a' is greater than 1.724.h, b =a.

  • In case of corner loading, maximum stresses are not produced at corner but they are produced at a certain distance X along the corner bisector. This is given by the relation:
     X = 2.58.(a.l)^1/2

 Here,    X = distance from apex of the slab corner to section of maximum stress along the corner bisector, cm.
   a= Radius of wheel load distribution, cm
    l = Radius of relative stiffness, cm.
Here is an image which shows you the formulas used to calculate the amount of stresses developed at the three critical positions due to the given wheel load P.

Rigid Pavement- Stresses at interior, edges and corners - Westergaard's theory

Thanks for you visit!

Monday, September 9, 2013

Part -2-GATE preparation - Transportation Engg. - One liners

5. What is the value of intermediate sight distance for a highway with a design speed of 65 kmph? Assuming the data for co-efficient of friction f = 0.36 and for reaction time t = 2.5 sec.
Ans: 182.8 m

6. The speed of overtaking and overtaken vehicles are 70 and 40 kmph respectively on a two way traffic road. If acceleration of overtaking vehicle is 0.99 respectively, then safe overtaking sight distance, assuming reaction time of 2 sec, will be  278 m.

7. What is the minimum length of overtaking zone for a design speed of 96 kmph assuming acceleration as 0.69 m/sec^2, reaction time as 2 sec and traffic as one way?   Ans: 1026 m  OSD = 3(d1+d2)

8. The radius of horizontal circular curve is 100 m. If design speed is 50 kmph and design co-efficient of lateral friction is 0.15, then super elevation required if full lateral friction is assumed to develop will be 0.047

9. What is the co-efficient of friction needed if no super elevation is provided for a horizontal circular curve of radius 190 m and design speed of 65 kmph?   Ans: 0.177

10. Ruling minimum radius of horizontal curve of a national highway in plain terrain for a ruling design speed of 100 kmph with e = 0.07 and f = 0.15, is close to  360 m.

11. Design rate of super-elevation for horizontal highway curve of radius 450 m for a mixed traffic condition, having a speed of 125 km/hour, is 0.07

Refer GK Publishers for elaborated answers.

Saturday, September 7, 2013

GATE 2014- Transportation Engineering - one liners - part 1

1. The safe stopping sight distance for design speed of 50 kmph two way traffic on a two lane road assuming co-efficient of friction as 0.37 and reaction time as 2.5 seconds is 61.4 m.

2. The stopping sight distance for design speed of 80 kmph for two way traffic on a single lane road. Assume co-efficient of friction as 0.35 and reaction time as 2 seconds, is 232.94 m.

3. What is the minimum sight distance required to avoid head on collision of two cars approaching from the opposite directions at 90 and 60 kmph? It is given that the reaction time is 2.5 seconds, co-efficient of friction is 0.7 and a break efficiency is 50 percent in either case.   Sol: 235.8 m.

4. What is the stopping sight distance on a highway at a ascending gradient of 5% for a design speed of 70 kmph assuming co-efficient of friction as 0.35 and reaction time as 2 seconds?  Sol: 87.14 m.

Reference: GATE 2013 by GK publishers (refer for elaborate answers)

Thursday, September 5, 2013

CBR(California Bearing Ratio) Test


CBR loading frame

  • Aim: To find out the CBR(California bearing ratio) value of the given soil sub-grade.
  • Apparatus: 
  1. CBR Apparatus
  2. soil sample with known OMC and MDD.
    CBR apparatus - accessories
  • Theory: California Bearing Ratio test was invented by California State Highway Department. This test is used to design the thickness of the flexible pavement. 
CBR value signifies the strength characteristics of the soil sub-grade which is compacted to the MDD using the OMC. The samples used for the testing are prepared in the laboratory. If a new pavement is to be constructed then, sample are prepared by compacting it with OMC and then sample is soaked in water for four days.

If the test is done for the overlay design then the sample is prepared by compacted it to the density of the soil at the site. Four days soaking is necessary in order to achieve the worst site conditions.
Higher the CBR value more is the strength of the soil sub-grade. Empirical charts are prepared by the IRC to find out the thickness of the flexible pavement corresponding to the given CBR value and for the given design wheel loading.

If the CBR value obtained with the 5 mm penetration exceeds the value obtained with the 2.5 mm penetration then this test is performed again and if the value are still same then CBR value at 5 mm is taken as the final value.

  • Procedure: 
    CBR apparatus
  1. Take the soil from the given soil sub-grade remove the gravel of size more than 20 mm and and find out its OMC.
  2. Compact the soil in three layers in the CBR mold, with 25 numbers of blows given to each layer.
  3. Put the surcharge weight and then immerse the sample in the water for four days.
  4. Put the sample with the surcharge weight on the loading base of the CBR apparatus.
  5. Apply the loading with a standard rate 1.25 mm/min with the 5 cm plunger and note down the load values corresponding to the penetrations of 1mm, 2 mm, 3 mm, 4 mm, 5 mm, 7.5 mm, 10 mm and 12 mm.
  6. Plot the graph and apply the correction if any.
  7. Repeat the test for two more samples.
  • Calculations: 
Check if there is any correction to be applied to the penetration and loading curve.
CBR value at 2.5 mm penetration = (Load at 2.5 mm penetration/ Standard load at 2.5 mm penetration i.e. 1370kg)*100
CBR value at 5 mm penetration = (Load at 5 mm penetration/ Standard load at 5 mm penetration i.e. 2055kg)*100
Use the CBR value at the 2.5 mm penetration if it is more than that at 5 mm penetration otherwise, repeat the test. If the value at the 5 mm penetration still comes out to be more, then use it.
  • Result: CBR value of the given soil sub-grade sample = .....%
Check the relevant books:

Wednesday, September 4, 2013

Aggregate Impact Value Test

AIM: to find the aggregate Impact value.

Aggregate to be used as road materials must possess some properties or characteristics. Toughness is one of the highly required property which is necessary for the aggregates to bear the impact loads. 

Road aggregates are applied with the impact loads a millions of times in their life as the road materials. So they must be tested for their toughness before they are used in the pavement layers. 
Toughness can be tested using a Impact testing machine, which is an arrangement to apply the impact loads on the aggregates just like they are applied on the roads. 
Materials which get fractured or crushed into smaller particles are not tough. In this test we will find out the percentage of the weight of the aggregate sample which gets crushed with respect to the total weight of the sample. This percentage is known as the aggregate impact value and more the aggregate impact value less is the toughness of the road aggregates and vice verse.  

If impact value is less than 10% then aggregate is said to be exceptionally strong, if it is in range of 10 to 20% then they are good, aggregates having impact value less than 35% are considered satisfactory by the IRC(Indian Roads Congress).

Apparatus Used:  Aggregate Impact Load Testing Machine, IS Sieves of size 12.5 mm; 10 mm and 2.36 mm. Electronic weighing balance, tray.

Suppose weight of the Total aggregate samples in the cylindrical mould( which passed through 12.5 mm Sieve and retained on 10 mm Sieve) = W1
Let weight of the crushed aggregates(Which pass through 2.36 mm IS Sieve) = W2
Impact value of the aggregates(%) = W2/W1 *100

Results: Aggregate Impact Value =       %

Tuesday, September 3, 2013

Engineering Surveys and the location of highway alignment

Location of the highway alignment is done after carrying out survey of the area, these surveys are called Engineering Surveys. 

We have to locate an alignment which fulfill the basic requirements like the path must be short, safe, economic, easy and useful. To check all these basic requirements we can carry out the

Engineering Surveys in the following phases:
  1.  Map Study
  2.  Reconnaissance Surveys
  3.  Preliminary Surveys
  4. Location Surveys
  •  Map Study: 
This is the first step of the Engineering survey, using a topographic map of the area under consideration, which can be availed from the Survey of India, we can propose different alternatives of the road alignment. 
This topographic map in general have a contour interval of around 30 m to 40 m. 

We can get the details of the natural and artificial features of the area using the topographic map, and accordingly we can suggest a numbers of alternatives for the road alignment. These routes are further studied in the Reconnaissance survey.
  •  Reconnaissance Survey: So in the second phase/step a survey team is headed to the area under study with the minor surveying instruments like Abney level, Tangent Clinometer etc. to do a rough survey of the area under study. 
The rough survey is done along the alternatives proposed in the map study and feasibility of the road alignment is checked along the different routes. 
Some of the routes may be cancelled out or they may be changed if they appear to impossible in this study. So finally they will have a set of routes which are to be further studies in the next step.
  • Preliminary Survey: In this step the alternative routes which are proposed after a rough survey in the second step are surveyed in details using some advanced instruments like levels, chain and theodolite. Aerial Photogrammetry is best suited for this type of survey.                                                                
      All the necessary details to carry out the comparative study of the different routes are collected and then finally we have to decide one alignment best suited for the alignment of the road. 
Here various details are found out along the stretches of the routes, which can also be found using the aerial techniques by taking photographs along the routes and then further processed to find out the final details of the area.                         
Different kind of surveys like, Soil investigations, cross sectioning and profiling, marine surveying, hydrology data collection, obligatory points, industries and  population surveys are necessary along the routes and only then it is possible to have a fair comparison of the different routes. 

So finally one among all of them is chose and drawings are prepared on the sheet which will show its alignment to be shifted on to the ground.

  • Location Survey: 
In this fourth phase of the Engineering Survey for the highway location, we have a drawing of the alignment and we have to go through the further two processes:
   (a) Location      (b) Detailed Survey

  •  Location:- Location of the center line of the road is done with very much precise instrument like Theodolite and Chain using the drawing prepared or the details gathered in the third step(i.e. Preliminary survey). This is done by staking the ground with the stakes inserted at the intervals of 50 m to 100 m in the plain area, 50 m to 75 m in the rolling terrain and 30 m to 50 m in the hills and steep terrain.                                                                                  
Pegs may driven at all the control points. At the curves control points, starting of the transition curve, starting of the circular curve and terminal of the circular curve and the terminal of the transition curve the pegs/stakes are driven into the ground to firmly locate these control points. Bench marks are located at and interval of 250 m and they are necessarily located at the sites of the cross drainage works.                                                        
  •   Detailed Survey: In this part we have carry out the detailed study of the final route using some very precise instruments like Theodolite and Chain to gather all the necessary data for the final estimation, design and preparing drawings using which the construction can be started. A detailed project report is to be prepared and all the necessary data is collected to prepare that report.
 So, the profiling, cross-sectioning and soil investigation are carried out very precisely. CBR values are also found to find out the design thickness of the pavement. After collecting the data a final drawing a report is prepared which concludes the highway planning part. 
Relevant books:

Monday, September 2, 2013

Basic Requirements of a Highway alignment on plain and hill roads


There are some basic requirements of the highway alignment in the plain and hill roads which must be fulfilled. In general the basic requirements are:

(1) Short: The alignment must be the shortest of the various alternatives available. Of course the shortest path between any two points is a straight line but the topography of the area or other factors may necessitate it do divert and take some other route, but as far as possible it should be kept minimum.
(2) Easy: Alignment should be such that the road must be easy to construct and easy to maintain or repair. If curves are of large radius and the gradient is gentle it would be easy to construct the road, rather than opposite.

(3) Safety: Safety is again the basic requirement of the highway alignment and special care must be taken to align the road in such a way that it must have the safe or minimum Sight distances and Radius of the curves, means the geometrical design features like Sight Distance, Radius of the curves and the gradient of the road must be given special attention.

(4) Economical: Road alignment must be designed to have the initial cost of construction, maintenance cost and the vehicle operation cost to a minimum. Also the locally available materials should be checked  before and it may decrease the over all cost. There must be a balance in the cutting and filling on the alignment of the road.

Some other basic requirements specially on the hill roads:
Hill roads have some other basic requirements also which govern the alignment of the hill roads:

(1) Drainage: Drainage of the road must be kept in mind and it must be insured that enough drainage structures can be built on the route. As far as possible alignment must avoid the drainage works means it must have the minimum numbers of the drainage works.

(2) Economy: Economy is governed by the numbers of the drainage works, cutting filling and the gradient.

(3) Safety: Safety is governed by the sight distance, superelevation and the design radius of the curves. It must be kept in mind that gradient must be kept below the ruling gradient. In hill roads special attention must be given to the side slopes, and thorough geological surveys must be carried out to ensure the safety while construction as well as while traffic movement.

(4) Minimum resisting length: The unnecessary rise and fall of the gradient must be minimized to reduce the cost and length of road.


Derivation of Mass moment of Inertia for a Solid Cone

Hi, Problem: Derive the Mass Moment of Inertia of a solid cone with given mass density and angle half at vertex equal to 35 degrees. If ...