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**PAVEMENT DESIGN**

Based on the structural behaviour, pavements are of following types.

**1. Flexible Pavements **

- Flexible pavement are those which have low or negligible flexural strength. The flexible pavement layers reflect the deformation of the lower layers on the surface of the laer.
- Flexible pavement consist of 4 components.

1. Soil subgrade

2. Sub base course

3. Base course

4. Surface course

- Flexible pavement layers transmit the vertical or compressive stresses to the lower layers by grain to grain transfer through the points of contact in the granular structure.
- Bituminous concrete, granular materials with or without bituminous binders, WBM, soil aggregate mixes etc. are common examples of flexible pavements.
- Flexible pavements are commonly designed using empirical charts or equations. There are also semi-empirical and theoretical methods.

**2. Rigid Pavements **

- Rigid pavements posses some worthy flexural strength or flexural rigidity.
- These transfer the load through slab action but not grain to grain as in case of flexible pavements.

1. cement concrete slab 2. base course 3. soil subgrade

- The rigid pavements are made of portland cement concrete either plain, reinforced or prestressed. The plain cement concrete are expected to take-up about 40 kg/cm2 flexural stress.
- These are designed using elastic theory, assuming pavement as an elastic plate resting over an elastic or a viscous foundation.

**3. Semirigid Pavements **

- When bounded materials like the pozzolanic concrete, lean cement concrete or soil cement are used then pavement layer has considerably higher flexural strength then the common flexible pavement layers, such pavements are called semirigid pavements.
- These materials have low resistance to impact and abrasion and therefore are used with flexible pavement surface course.

**FUNCTIONS OF PAVEMENT COMPONENTS****1. Soil Subgrade **

The pavement load is ultimately taken by soil subgrade hence in no case it should be over stressed and top 50 cm layer of soil subgrade should be well compacted at O.M.C. (Optimum moistore content)

- Common strength tests used for evaluation of soil subgrade are :

1. CBR test

2. California resistance value test

3. Triaxial compression test

4. Plate bearing test

**2. Sub-base and Base Course**

- These are broken stone aggregates. It is desirable to use smaller size graded aggregates at sub base course instead of boulder stones.
- Base and sub base courses are used under flexible pavements primarily to improve load supporting capacity by distribution of the load through a finite thickness.
- Base courses are used under rigid pavements for

1. preventing pumping

2. protecting the subgrade against frost action.

** 3. Wearing Course **

- Purpose of this course is to give smooth riding surface. It resists pressure exerted by tyres and take up wear and tear due to traffic. It also offers water tightness.
- The stability of wearing course is estimated by Marshall stability test where in optimum % of bituminous material is worked out based on stability density. VMA & VFB. Plate bearing test and Banklemann beam test are also some times made use, for evaluating the wearing course and the pavement as a whole.

**DESIGN FACTORS FOR FLEXIBLE PAVEMENTS**

1. Design wheel load

2. Subgrade soil

3. Climatic factors

4. Pavement component materials

5. Environmental factors

1. Design Wheel Load Following are the important wheel load factors.

(a) Maximum wheel load

- Maximum legal axle load as specific by IRC is 8170 kg with a maximum equivalent single wheel load of 4085 kg.

Total load influences the quality of surface course.

Do you know ?

- Vertical stress computation under a circular load is based on Boussineqâ€™s Theory.

Notation have their usual meaning.

**(b) Contact Pressure **

- Tyre pressure of high magnitudes demand high quality of materials in upper layers in pavements however total depth of pavement is not governed by tyre pressure.
- Generally wheel load is assumed to be distributed on circular area but it is seen that contact area in many cases are elliptical.
- Following are the terms which are commonly used with reference to tyre pressure.

(a) Tyre pressure

(b) Inflation pressure

(c) Contact pressure - Tyre pressure and inflation pressure mean exactly the same. The contact pressure is found more than tyre pressure when the tyre pressure is less than 7 kg/cm
^{2}and it is viceversa when the tyre pressure exceeds 7 kg/ cm^{2.}

- Rigidity factor R.F. = Contact Pressure/ Tyre pressure

You can assume contact pressure = 7 kg/cm^{2} then if tyre pressure = 7 kg/cm^{2}

âˆ´R.F. = 1

If tyre pressure < 7 kg/cm^{2}, R.F. > 1

If tyre pressure > 7 kg/cm^{2}, R.F. < 1

- The rigidity factor depends upon the degree of tension developed in the walls of the tyre.

**(c) Equivalent single wheel load (ESWL)**

- The effect on the pavement through a dual wheel assembly is not equal to two times the load on any one wheel. The pressure at a depth below the pavement surface is between the single load and two times load carried by any one wheel.

- Load dispersion is considered at 45Â°. Let d be the clear gap between the two wheels and S be the spacing between the centre of the wheels and â€˜aâ€™ be the radius of the circular contact area of each wheel, then S = d + 2a.
- Upto the depth (d/2) each wheel load P actsindependently after this over lapping takes place. At depth 2S and above the stresses induced are due to the effect of both wheels as the area of overlap is considerable so that total stresses due to the dual wheels at any depth greater than 2S is considered to be equivalent to a single wheel load of magnitude 2P, though this will be slightly higher than actual value.
- ES WL is the single wheel load which produces the same value of maximum stresses at the depth Z as the dual wheel assembly.

ESWL can be determined graphically.

Two points A and B are plotted on the loglog graph with coordinates of (P, (d/A)),B(2p,2S) 2

line AB is a plot which isthe locus of points where any single wheel load is equivalent to a certain set of dual wheels.

**(d) Repetition of loads**

- If the pavement structure fails with N
_{1}no. of repetitions of P_{1}kg load and similarly if N_{2}number of repetitions of P_{2}kg load can also cause failure of the same pavement structure then P_{1}N_{1}and P_{2}N_{2}are equivalent. - If a pavement thickness required for 10
^{6}repetitions is â€˜tâ€™ then pavement thickness required for failure at one repetion is t/4.

**(e) Elastic Modulii**

- Elastic modulii of different pavement material can be evaluated. Mainly plate bearing test is employed for this purpose.
- If Î” is maximum vertical deflection of the flexible plate then

If rigid circular plate is used instead of flexible then

Where a = radius of plate p = pressure at deflection E_{s }= youngâ€™s modulus of pavement material**Frost Action **

- Frost action refers to the adverse effect due to frost heave. Due to continuous supply of water from capillary action at sub freezing temperature leads to formation of frost heave, the non uniform heaving may cause damages to the pavement this heaving and thawing leads to undulations.
- Factors on which frost action depends may be 1. Frost susceptible soil. 2. Depressed temperature below freezing point. 3. Supply of water 4. Cover
- To reduce the damage due to frost action proper surface and sub surface drainage system should be provided.
- Capillary cutoffs can also be provided to reduce the adverse effect of frost action by soil stabilization.

**DESIGN OF FLEXIBLE PAVEMENTS**

- Various approaches for flexible pavement design may be classified in to three broad groups.

**(a) Empirical Methods **

- These are based on physical properties and strength parameter of soil subgrade.
- The group index method, CBR method, Stabilometer method and Mc-leod method etc. are empiricial methods.

**(b) Sem i Empirical or semitheoretical method **

- These methods are based on stress Strain function and experience. eg., Triaxial test method.

**(c) Theoretical methods **

- These are bas ed on mathematical computations for e.g. Burmister method is based on elastic two layer theory.

**Group Index Method **

- The higher the G.I. value weaker is the soil subgrade and for a constant value of traffic volume, the greater would be the thickness requirement of the pavement.

Sub Grade | Group index value |

Good | 0-1 |

Fair | 2-4 |

Poor | 5-9 |

Very poor | 10-20 |

- This is an empiricial method based on physical properties of the subgrade soil. This method does does not consider the strength characteristics of the subgrade soil.
- The quality of the sub base and base course is not considered here, emphasis is given to only subgrade soil type.
- Traffic volume is classified as Light less than 50 Veh./day Medium 50 to 300 Veh./day Heavy > 300 Veh./day
- G.I. value is related to thickness by design charts.

**California Bearing Ratio Method **

- This is also an empirical method and has simplicity in procedure.
- CBR test data are co-related with the pavement thickness and can be calculated by

This expression is applicable only when the CBR value of the subgrade soil is less than 12%.

t = pavement thickness in cm.

P = wheel load in kg CBR = California Bearing Ratio (%) A = contact area in cm^{2 }

- CBR method is based on the s trength parameters of subgrade soil and subsequent pavement material.

**IRC Recommendations**

1. CBR test should be performed on remoulded soils in the laboratory, insitu test are not recommended for design purpose.

2. The soil should be compacted at OMC (Optimum moisture content) to proctor density.

3. Test samples should be soaked in water for 4 days period before testing. However in dry zone (< 50 cm rainfall) it is not necessary to soak.

4. At least 3 samples should be tested on each type of soil at the same density and moisture content, if variation is more than permissible value, an average of six samples should be considered.

Permissible var iations | CBR% |

3% | up to10% |

6% | 10 to 30% |

10% | 30 to 60% |

5. The top 50 cm of sub grade should be compacted at least up to 95 to 100% proctor density

6. Following formula may be used in case estimating future heavy vehicles in view of growth rate for design.

A = P [1 + r]^{(n + 10)}

Where, A = number of heavy vehicles/day for design (weight > 3 tonnes).

P = No. of heavy vehicles per day at last count. r = annual rate of increase of vehicles n = No. of years between the last count and the year of completion of construction.

- P should be seven days average and r can be taken as 7.5% for roads in rural areas.

7. The deisgn thickness is considered applicable for single axle loads upto 8200 kg and tandem axle loads up to 14500 kg. For higher axle loads, the thickness values should be further increased.

8. When sub base course materials contain substantial proportion of aggregates of size above 20 mm, the CBR value of the materials would not be valid for the design of subsequent layer above them.

**Limitations **

- The CBR method gives the total thickness requirement of the pavement above a subgrade and this thickness value would remain same irrespective of the quality of materials used in component layers. Thus the component of materials should be judiciously chosen for durability and economy.

**California Resistance Value Method** Total thickness of pavement is given by

Where, K = numerical constant = 0.166 T.I. = traffic index = 1.35 (EWL)^{0.11}

R = Stabilometer resistance value C = Cohesionmeter value.

The annual value of (EWL) here is the accumulated sum of the products of the constants and the number of the axle loads.

Equivalent C Value

Where t_{1} and t_{2} are thickness of any two pavement layer and C_{1} and C_{2} are their corresponding chohesionmeter values.

Material Soil cement base course Bituminous concrete Open graded bituminous mix Gravel base course

Material | C Value |

Soil cement base course | 120 â€“ 130 |

Bituminous concrete | 60 â€“ 62 |

Open graded bituminous mix | 22 â€“ 30 |

Gravel base course | 15 |

**Tri-axial Method **

- The pavement thickness Ts consisting of materials with modulus Es is given by

The value of traffic coefficient (X)

X = (1/2) For ADT = 40 to 400X = 1

For ADT = 1201 to 1800 X = 2

For ADT = 13501 to 20000

- The value of Rainfall coefficient (Y) Y = 0.5, For avg. rainfall of 38 to 50 cm Y = 1.0, For avg. rainfall of 101 to 127 cm
- The pavement and subgrade are considered two layer system hence stiffess factor has to be introduced to take into account the different values of modulus of elasticity of the two layers.

**McLeod Method**

- Based on plate load test results an empirical design equation was recommended as

Where, T = Required thickness of gravel base, (cm)

P = Gross wheel load (kg)

S = total subgrade support, (kg) [for same contact area, deflection and repetition of load P]

K = base course constant

- The s ubg rade s upp ort S for the d esign is calculated from the support measured or calculated for 30 cm deflection and 10 repetions.

**Burmisterâ€™s Layered Method**

- The flexible pavement is made of different layers and top layers has highest modulus of elasticity constant E.

**Assumptions made are : **

1. Material in the pavement layers are isotropic, homogenous and elastic. The pavement forms stiffer reinforcing layer than under lying layer.

2. Surface layers is infinite in horizontal direction but infinite in vertical direction; the under lying layer in two layered system is infinite in both directions.

3. The layers are in continuous contact; the top layer is free of shearing and normal stresses out side the loaded area.

4. This approach utilizes reinforcing action pavement layer in which = 10

Where E_{p} = modulus for pavement E_{s} = modulus for soil subgrade

**Design of Rigid Pavements**

- Cement concrete pavements have the load carrying capacity mainly due to rigidity and high modulus of elasticity.
- In the analysis Westergaard used the rigid plate of diameter 75 cm to find modulus of subgrade reaction K.

**Relative stiffness of slab to subgrade :**

- The subgrade material offers resistance to slab deflection which depends on stiffness of the subgrade material. The tendency of slab delfection depends upon stiffness of slab, hence relative stiffness of slab to that subgrade can be defined.
- Radius of relative stiffness

Modulus of Elasticity of cement concrete pavement kg/cm^{2}.

Âµ = Poissonâ€™s ratio for concrete = 0.15

h = slab thickness (cm).

K = Modulus of subgrade reaction. (kg/cm^{3})

**Stresses on Rigid Pavement**

1. Wheel load stresses

2. Temperature stresses

These can be of two types

(a) Warping stresses

(b) Frictional stresses.

**Critical Load Positions **

(a) Interior loading : Load is applied in the interior of the slab.

(b) Edge loading : Load is applied at the edge of slab other than corners.

(c) Corner loading : Centre of the load is located on bisector of the corner angle and loaded area is at the corner touching the two corner edges.

**TEMPERATURE STRESS**

- Westergaard gave the concept of temperature analysis

(a) warping stresses

- Due to daily variation in temperature reversal of stresses takes place due to heating and cooling of pavement. The maximum temperature difference occurs in evening hence warping stresses are predominant in late evening.
- The magnitude of warping stresses are maximum at the interior region and are minimum at the corner region.
- When the slab is warped down in the day time, the warping stresses are tensile in nature at the bottom of the slab. During night when slab is warped up the tensile stresses are developed at the top of the pavement slab.

- Warping stresses can be calculated as given by Bradburry.

**Critical Stress Combination **

1. During Summer

- Critical combination occurs during mid day.

The load stress at edge region is higher.

Critical combination of stresses = load stress + warping stress-frictional stress

- First two are tensile while frictional stresses are compressive.

**2. During Winter **

- Critical combination occurs at bottom fibre during mid day. Frictional stresses are also tensile due to contraction.

Stresses at edge region are critical = load stress + warping stress + frictional stress

- Since the range of temperature difference is lower during winter than summer, therefore summer combination is worst.
- At corner region, the critical combination occurs at the top fibre of the slab, when the slab warps down wards during the mid nights.

There is no frictional stress at corner region.

The critical combination = load stress + warping stress (at corner region)

Do you know ?

The critical combination at the edge region is higher than the corner under the identical conditions of pavement, load and temperature.

**Design of joints in cement concrete pavement Joint may be classiofied as** :

**1. Transverse Joints**

These are further classified as :

(a) Expansion joint

(b) Contraction joint

(c) Warping joint

(d) Construction joint

**2. Longitudinal Joints **The location of these joints are shown.

**Expansion Joint**

- These are provided to allow for expansion of the slab due to rise of temperature. These also permit the contraction of slabs.
- The approximate gap width for this type of joints is from 20 to 25 mm.

- These joint are reinforced at suitable interval projecting in the concrete up to 60 cm. These reinforcing rods are called dowel bars.
- IRC recommends 2.5 cm in diameter dowel bars of length 50 cm to be spaced at 20 cm in the case of 15 cm thick slabs and spaced at 30 cm in the case of 20 cm thick slabs, the design load being 5100 kg.

**Spacing of Expansion Joint **

- These are provided at interval of 50 to 60 meter for smooth interface laid in winter and 90 to 120 meters for smooth interface laid in summer. IRC has recoomended for rough interface the spacing between expansion joint should not be > 140 m.
- The joint filter may be assumed to compressed up to 50% of its thickness and therefor the expansion gap should be twice the allowable expansion in concrete is 2Î´'

If Î´^{1} be the half of the joint width, the spacing of expansion joint Le is given by

Where, Î´' is in cm.

L_{e} is in m.

**Contraction Joints **

- These are provided to permit the contraction of the slab. These joints are spaced closer than expansion joints.
- As per IRC, maximum spacing of contraction joints in reinforced C.C. slabs is 4.5 m and in reinforced slab of thickness 20 cm is 14 m.

**Warping Joints**

- Warping joints are provided to relieve stresses due to warping. These are known as hinged joints.
- Longitudinal joints with tie bars fall in this class of joint.
- These a re rar ely need ed if exp ansion and contraction joints are well designed.

**Longitudinal Joints **

- These are provided in cement concrete pavements which have width over 4.5 m, to allow differential shrinking and swelling due to rapid change in moisture, under the edges than under the centre of road.
- These prevent longitudinal cracking in the centre of the pavement. This type of joint acts as a hinge and helps to maintain the two slabs together at the same level.
- Tie bars are provided to hold the adjacent slabs together.
- IRC recoomends to use plain butt with tie bars.

**JOINT FILLER****Properties Required **(a) Compressibility (b) Elasticity (c) Durability** **

**Type of Joint Filler** (a) Soft wood (b) Impregnated fibre board (c) cook or cork bound with bitumen Do you know ?

The bitumen content specified by IRC is 35%** **

**JOINT SEALER**

- Properties desirable. (a) Adhesion to cement concrete edge. (b) Extensibility without fracture. (c) Resistance to ingress of grit. (d) Durability
- Bitumen and Rubber bitumen compound are in frequent use of higher viscosity grade. Air blow bitumen has less susceptibility to the temperature change.

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