Flexible

IRC:58-2011

DESIGN OF RIGID PAVEMENTtransportation ENGINEERING GROUPDEPARTMENT OF CIVIL ENGINEERINGINDIAN INSTITUTE OF TECHNOLOGY ROORKEEROORKEE 247 667, Uttarakhand, INDIA

AUTUMN :2012-2013GUIDELINES FOR THE DESIGN OF PLAIN JOINTED RIGID PAVEMENTS FOR HIGHWAYSTHIRD REVISION

SCOPEThe Guidelines Cover The Design Of Plain Jointed Cement Concrete Pavements With Or Without Tied Concrete ShouldersDr.G.D. Ransinchung R.N.1 IRC:58-2011

DESIGN OF RIGID PAVEMENTtransportation ENGINEERING GROUPDEPARTMENT OF CIVIL ENGINEERINGINDIAN INSTITUTE OF TECHNOLOGY ROORKEEROORKEE 247 667, Uttarakhand, INDIAAUTUMN :2012-2013The Guidelines Are Applicable To Roads

Having average Daily Commercial Traffic Volume More Than 450 (Vehicles With Laden Weight Exceeding 3 Tonne)

- For low-volume rural roads, IRC:SP:62

2 IRC:58-2011


AUTUMN :2012-2013The present design guidelines considered the following components:

the spectrum of axle loads as per present day vehicle fleet

cumulative fatigue damage due to the combined effect of load and pavement temperature variations

3 IRC:58-2011


AUTUMN :2012-2013

The guidelines also include procedure for design of pavements with (a) widened outer lane, (b) tied concrete shoulder, (c) pavements bonded to cemented subbase, (d)design of longitudinal joints, (e) expansion and contraction joint as well as longitudinal, (f) expansion and contraction joints4


AUTUMN :2012-2013

Salient features of the IRC:58-2011 are:

(a) Design of pavements considering the combined flexural stress under the simultaneous action of load and temperature gradient for different categories of axles

(b) Design for bottom-up fatigue cracking caused by single and tandem axle load repetitions

(c) Design for top-down fatigue cracking caused by single, tandem and tridem axle load repetitions5


AUTUMN :2012-2013

Salient features of the IRC:58-2011 are:

(d) Consideration of in-built permanent curl in the analysis of flexural stresses

(e) Design guidelines for pavements without concrete shoulders and tied concrete shoulders

(f) Consideration of concrete slabs with unbounded as well as bonded cement bound subbase (g) Design of pavements with widened outer lanes6

Concrete pavement typestransportation ENGINEERING GROUPDEPARTMENT OF CIVIL ENGINEERINGINDIAN INSTITUTE OF TECHNOLOGY ROORKEEROORKEE 247 667, Uttarakhand, INDIA

AUTUMN :2012-2013

Several types of concrete pavements have been used in different countries depending upon the

ClimateAvailability of materialsSoil typesExperience , and Traffic 7

Typical cross sections of a few pavementstransportation ENGINEERING GROUPDEPARTMENT OF CIVIL ENGINEERINGINDIAN INSTITUTE OF TECHNOLOGY ROORKEEROORKEE 247 667, Uttarakhand, INDIA

AUTUMN :2012-2013

8

Factors governing designtransportation ENGINEERING GROUPDEPARTMENT OF CIVIL ENGINEERINGINDIAN INSTITUTE OF TECHNOLOGY ROORKEEROORKEE 247 667, Uttarakhand, INDIA

AUTUMN :2012-2013

(A) The main factors governing design of concrete pavements are: Design periodDesign commercial traffic volumeComposition of commercial traffic in terms of (a) single (b) Tandem (c) tridem, and (d) multi-axles9


AUTUMN :2012-2013

(B) Axle Load Characteristics Though the legal axle load limits in India are

For single axle = 10.2 tonnes (100kN)For tandem axles = 19.0 tonnes (186 kN)For tridem axles = 24.0 tonnes (235kN)

A large number of axles operating on NHs carry much heavier loads than the legal limits.10


AUTUMN :2012-2013

(B) Axle Load Characteristics

Therefore, data on axle load spectrum of the commercial vehicles is required to estimate the repetitions of

Single (ii) tandem and (iii) tridem axles

in each direction expected during the design period11


AUTUMN :2012-2013


Minimum % of CV to be weighed should be

10 percent for volume of CVPD > 6000

15 percent for volume of CVPD b/w 3000 to 6000

20 percent for volume of CVPD < 300012


AUTUMN :2012-2013


Axle load survey may be conducted for a continuous 48-hour period

The vehicle to be surveyed shall be selected randomly to avoid bias

If the spacing of consecutive axles (wheel base) is more than 2.4 m, each axle may be considered as a single axle13


AUTUMN :2012-2013


The interval at which axle load groups should be classified for fatigue damage analysis are:

Single axle = 10 kNTandem axle = 20 kNTridem axle = 30 kN

14


AUTUMN :2012-2013


Tyre inflation pressures = 0.7 MPa to 1.0 MPa as most of the CV maintained this pressure

Stresses in concrete pavements having thickness of 200 mm or higher are not affected significantly by the variation of tyre pressure

Hence, a tyre pressure of 0.8 MPa is normally adopted for design purpose15


AUTUMN :2012-2013

Wheel Base Characteristics

Information on typical spacing b/w successive axles of CV is necessary to identify the proportion of axles that should be considered for estimating * top-down fatigue cracking caused by axle loads during night period when the slab has the tendency of curling up due to negative temperature differential This detail should be collected during traffic survey16


AUTUMN :2012-2013

Wheel Base Characteristics If the spacing b/w any pair of axles is less than the spacing of transverse joints, such axles need to be considered in the design traffic for computing top-down fatigue cracking damage

Wheel bases of trucks of different models generally range from 3.6m to more than 5.0m

Whereas commonly used spacing of transverse joint is 4.5m17


AUTUMN :2012-2013

Wheel Base Characteristics

Thus, axles with spacing of more than 4.5 m are not expected to contribute to top-down fatigue cracking

However, if the actual spacing of transverse joint is different from 4.5 m, design traffic for estimation of top-down cracking damage may be selected appropriately

The % of CVs with spacing b/w the front and the first rear axle less than the proposed spacing of transverse joints in the concrete slab should be established from axle load survey18


AUTUMN :2012-2013

(d) Design Period

Generally, rigid pavements are design to have a life of 30 years or more.

However, the design engineers should use his/her judgment about the design period taking into consideration factors such as (i) traffic volume (ii) uncertainty of traffic growth rate (iii) capacity of the road etc. 19


AUTUMN :2012-2013

(e) Traffic consideration

Design lane:

The lane carrying the max. number of heavy commercial vehicles is termed as design lane Each lane of a two-way two lane highway and the outer lane of multi-lane highways can be considered as design lanes

20


AUTUMN :2012-2013


Design traffic: Assessment of average daily traffic should normally be based on seven-day 24-hour count made in accordance with IRC:9 The actual value of annual rate of growth r of CV should be determined using appropriate methods

21


AUTUMN :2012-2013


Design traffic: As per IRC: SP: 84, annual growth rate of CVs shall be taken to be a minimum of 5%

Normally, 7.5% value is adopted in the absence of actual data

22


AUTUMN :2012-2013

(e) Traffic consideration Design traffic: The traffic counts and the corresponding traffic estimates should indicate the day and night traffic trends because (i) the traffic loading during the day hours is generally responsible for bottom-up cracking (ii) the traffic loading during the night hours is generally responsible for top-down cracking 23


AUTUMN :2012-2013

(e) Traffic consideration Design traffic:

When the tyre imprint of the outer wheel touches the longitudinal edge the edge flexural stress caused by axle loads for bottom-up cracking is the maximum 24


AUTUMN :2012-2013

(e) Traffic consideration Design traffic:

When the tyre position is away by 15cm from the longitudinal edge

stress in the edge region is reduced substantially. 15 cm25


AUTUMN :2012-2013

(e) Traffic consideration Design traffic: The edge flexural stress is small when the wheels are close to the transverse joints. 15 cm Typical lateral distribution characteristics of wheel paths of CVs observed on Indian highways indicate that very few tyre imprints of moving vehicles are tangential to LE. 26


AUTUMN :2012-2013

(e) Traffic consideration Design traffic: Some multi-lane divided highways have 8.5m to 9.0m wide carriageways with a single longitudinal joint in the centre.

The lane marking in this cases do not coincide with the longitudinal joint resulting in a larger portion of wheel paths being positioned close to the longitudinal joint compared to the situation where the lane markings match with longitudinal joints27


AUTUMN :2012-2013

(e) Traffic consideration Design traffic: Taking into consideration these issues, it is recommended that 25% of the total two-way commercial traffic may be considered as design traffic for two-lane two-way roads for the analysis of bottom-up cracking

Similarly, the design traffic for top-down cracking analysis will be a portion of the design traffic considered for bottom-up cracking analysis Only those CVs with the spacing b/w the front axle and the first rear axle less than the spacing of the transverse joints should be considered for top-down cracking28


AUTUMN :2012-2013

(e) Traffic consideration Design traffic: In case of new highway links, where no traffic count data is available

data from roads of similar classification and importance may be used to predict the design traffic intensity29


AUTUMN :2012-2013

(e) Traffic consideration Design traffic: In case of new highway links, where no traffic count data is available

data from roads of similar classification and importance may be used to predict the design traffic intensity30


AUTUMN :2012-2013

(e) Traffic consideration Design traffic: The cumulative number of CVs during the design period may be estimated from the following expression C =365 x A { (1+r)n -1} rC = Cumulative no. of CVs during the design periodA = Initial No. of CVs per day in the year when the road is opened to trafficR = Annual rate of growth of CT volumen = Design period in years---------- (1)31


AUTUMN :2012-2013

(f) Temperature Consideration Temperature differential: Temperature differential b/w the top and bottom fibres of concrete pavements causes the concrete slab to curl, giving rise to stresses

The temperature differential is a function of solar radiation received by the pavement surface, wind velocity, thermal diffusivity of concrete, latitude, longitude and elevation of the place and thus affected by geographical features of the pavement location. 32


AUTUMN :2012-2013

(f) Temperature Consideration Temperature differential: In the absence of local data, the maximum temperature differential values given below may be adopted

33


AUTUMN :2012-2013

(f) Temperature Consideration Temperature differential: The variation of temperature with depth is non-linear during the day time and nearly linear during night hours

The maximum temperature differential during the night is nearly half of the day time maximum temperature differential

34


AUTUMN :2012-2013

(f) Temperature Consideration Temperature differential: Temperature differentials are

positive when the slab has the tendency to have a convex shape during the day hours and negative with a concave shape during the night

The axle load should be computed for fatigue analysis when the slab is in a curled state due to the temperature differential during day as well as night hours 35


AUTUMN :2012-2013

(f) Temperature Consideration Zero stress temperature Cement concrete slabs laid during day time will have high positive temperature differential due to (i) intense solar radiation (ii) high air temperature (iii) chemical reaction

In spite of this positive temperature differential occurring in concrete laid during day time, the slab remains flat during the hardening stage because of its plastic stage 36


AUTUMN :2012-2013

(f) Temperature Consideration Zero stress temperature The slab is stress free in this condition with high temperature on the top surface and lower at the bottom fibre and the corresponding temperature gradient is known as Zero stress temperature gradient

Research on in-service concrete pavements indicates that exposure of fresh concrete to sun and high air temperature during the hardening stage causes building of permanent curl in the concrete pavements which is nearly equivalent to the curl caused by a negative temperature differential of about 50C37


AUTUMN :2012-2013

(f) Temperature Consideration This equivalent negative temperature differential has to be added algebraically to the actual temperature differential prevailing at any time

Field investigations on existing pavements located in different regions of the country will be necessary to establish the zero stress temperature gradient for future guidance38


AUTUMN :2012-2013

(f) Temperature Consideration If the max. positive temperature differential during the day time is 200C, the temperature differential for stress computation can be taken as 150C

During the night hours, if the temperature differential is 100C, the total effective negative temperature differential can be taken as 150C (100C+50C)39


AUTUMN :2012-2013

(f) Temperature Consideration Since it is too cumbersome to carry out hourly cumulative fatigue damage analysis, it is suggested that the maximum positive and negative temperature differentialrespectively may be assumed to be constant for

the six hour period during the day b/w 10AM and 4PM and for the six hour period

b/w 0AM to 6AM during night hours40


AUTUMN :2012-2013

(f) Temperature Consideration The slab may be assumed to be free of warping stresses for the remaining 12 hours for the purpose of fatigue damage analysis as the fatigue damage caused by the combined action of load and temperature differential will be insignificant during this period41


AUTUMN :2012-2013

(g) Soil characteristics (embankment soil, subgrade and subbase) CBR of embankment soil placed below the 500 mm selected subgrade should be determined for estimating the effective CBR of subgrade and its k value for designEmbankment soil42


AUTUMN :2012-2013

(g) Soil characteristics (embankment soil, subgrade and subbase) SubgradeThe subgrade is usually considered as a Wrinkler foundation, also known as dense liquid foundation

In Wrinlker model, it is assumed that the foundation is made up of springs supporting the concrete slab

The strength of subgrade is expressed in terms of modulus of subgrade reaction (k). 43


AUTUMN :2012-2013

44


AUTUMN :2012-2013

(g) Soil characteristics (embankment soil, subgrade and subbase) SubgradeThe modulus of subgrade reaction (k) is defined as the pressure per unit deflection of the foundation as determined by plate load tests.The k-value is determined from the pressure sustained at a deflection of 1.25 mmAs the k value is influenced by test plate diameter, the standard test is to be carried out with a 750 mm diameter plate45


AUTUMN :2012-2013

Modulus of subgrade reaction (k-value) 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/cm246


AUTUMN :2012-2013

(g) Soil characteristics (embankment soil, subgrade and subbase) A frequency of one test per km is recommended for assessment of k-value

If the foundation changes with respect to subgrade soil, type of subbase or the nature of formation (cut or fill) then additional tests may be conducted

Though 750mm is the standard diameter, smaller diameter plate can be used in the case of homogenous fdn from practical consideration and the test47


AUTUMN :2012-2013

(g) Soil characteristics (embankment soil, subgrade and subbase) diameter, smaller diameter plate can be used in the case of homogenous fdn from practical consideration and the test value obtained with plates of smaller diameter ay be converted to the standard 750mm plate value

K750 = k (1.21 + 0.078) ----- (2)

= plate diameter (m)K = Modul of sub reaction (MPa/m) with plate dia 48


AUTUMN :2012-2013

(g) Soil characteristics (embankment soil, subgrade and subbase) Since the k-value cannot be determined in the field at different moisture contents and densities, CBR tests may be carried out. In addition to that plate load test is time-consuming and expensive and, therefore, the design k-value is often estimated from soaked CBR value.

The relationship between the CBR and k-value for homogenous soil subgrade is given in Table 1. 49


AUTUMN :2012-2013

(g) Soil characteristics (embankment soil, subgrade and subbase) Since the k-value cannot be determined in the field at different moisture contents and densities, CBR tests may be carried out. In addition to that plate load test is time-consuming and expensive and, therefore, the design k-value is often estimated from soaked CBR value.

The relationship between the CBR and k-value for homogenous soil subgrade is given in Table 1. 50


AUTUMN :2012-2013

Table 1. Soaked CBR (%)2345710152050100K-value (MPa/m)212835424855626914022051


AUTUMN :2012-2013

If the CBR of the 500 mm thick compacted subgrade is significantly larger than that of the embankment below it,

the effective CBR of the subgrade can be estimated from Fig. 1

A minimum subgrade CBR of 8 percent is recommended fro design52


AUTUMN :2012-2013

Fig. 153


AUTUMN :2012-2013

The in-situ CBR of the subgrade soil can also be determined quickly from the Dynamic Cone Penetrometer (600 Cone) tests using the following relationship (ASTMD6951)

Log10 = CBR = 2.465 1.12log10 NDCP ------- (3)

Where NDCP = rate of cone penetration (mm/blow)54


AUTUMN :2012-2013

The modulus of subgrade reaction of the subgrade of an in-service pavement or of a prepared foundation can also be determined by conducting Falling Weight Deflectometer (FWD) tests.

The k-value of the subgrade backcalculated from FWD test data is the dynamic k-value

The corresponding static k-value, which should be used for analysis, can be estimated as 50% of the dynamic k-value obtained from FWD test

55


AUTUMN :2012-2013

It is advisable to provide filter and drainage layers above the subgrade for drainage of water to prevent

Excessive softening of subgrade & subbase and Erosion of the subgrade and subbase particularly under adverse moisture condition and heavy dynamic loadsSynthetic geo-composite layer can also be used at the interface of subgrade and granular subbase layer for filtration and drainageIt will not allow migration of fine particles of subgrade soil to the granular drainage layer above56


AUTUMN :2012-2013

Subbase

The main purpose of the subbase is to provide a uniform, stable and permanent support to the concrete slab laid over it

It must have sufficient strength so that it is not subjected to disintegration and erosion under heavy traffic and adverse environmental conditions such as excessive moisture, freezing and thawing.

57


AUTUMN :2012-2013

Subbase

In the light of these requirements, subbase of Dry Lean Concrete (DLC) having a 7-day average compressive strength of 10 MPa determined as per IRC-SP:49 is recommended.

Minimum recommended thickness of DLC for major highways is 150 mm58


AUTUMN :2012-2013

Subbase

In the case of problematic subgrades such as clayey and expansive soils appropriate provisions shall be made for blanket course in addition to the subbase as per relevant stipulations of IRC:15.

Effective k-values of different combinations of subgrade and subbase (untreated granular and cement treated granular) can be estimated from Table 2.59


AUTUMN :2012-2013

Table 260


AUTUMN :2012-2013

Table 361


AUTUMN :2012-2013

Separation layer b/w DLC and concrete slab

The interface layer b/w the concrete slab and the DLC layer can be made smooth to reduce the inter layer friction thereby allowing relative movement b/w the slab and DLC layer

A de-bonding interlayer of polythene sheet having a minimum thickness of 125 micron is recommended as per the practice in India62


AUTUMN :2012-2013

Separation layer b/w DLC and concrete slab

Wax based compound in place of plastic sheet has popularly been used with success in most countries including India

63


AUTUMN :2012-2013

International Practice on Use of De-bonding layer over stabilized/cemented subbase

Concrete slabs expand and contract with temperature and moisture changes(ii) High strength stabilized subbase layers have a rough texture offering high frictional restraint to the concrete pavement movement causing cracking at the early stages when the concrete is weak(iii) The most common practice has been use of two layers of wax emulsion(iv) Choke stone has been used in many projects in USA as a de-bonding layer. It is a small size uniformly graded a stone layer usually 13-25 mm thick below the PQC slab64


AUTUMN :2012-2013

(h) Concrete strength

Flexural strength of concrete is required for the purpose of design of concrete slab

This parameter can be obtained after testing the concrete beam as per procedure given in IS:516

Alternatively, it can be derived from the characteristics compressive strength of concrete as per IS 456-2000

65


AUTUMN :2012-2013


Fcr = 0.7 x fck ---- (4) Fcr = flexural strength (modulus of rupture), MPaFck = characteristics compressive cube strength of concrete, MPa

Usually, concrete design is based on 28 days strength

In the case of concrete pavement, 90 days strength can be permitted in view of the fact that during initial period of 90 days, the number of repetitions of load is very small and has negligible effect on cumulative fatigue damage of concrete

66


AUTUMN :2012-2013


Increasing the 28 days flexural strength by a factor of 1.10 is recommended to get 90 days strength

In no case 28 days flexural strength of pavement quality concrete should be less than 4.5 MPa

67


AUTUMN :2012-2013


Target mean flexural strength to be achieved while designing the Mix should be such that there is 95% probability, that the characteristic strength would be achieved when the Mix is produced in the field

The target mean strength is given by the following Eqn.

TM FCr = Fcr + Za ------ (5)

68


AUTUMN :2012-2013


Where,

Fcr = characteristics flexural strength at 28 days, MPaTM Fcr = target mean strength at 28 days, MPaZa = a factor corresponding to the desired confidence level, which is 1.96 for 5% tolerance level

= standard deviation of field test samples , MPa69


AUTUMN :2012-2013

Modulus of elasticity of concrete & poissons ratio of concrete

The elastic modulus increases with increase in strength

Poissons ratio decreases with increase in the modulus of elasticity

A 25% variation in E & values will have only a marginal effect on the flexural stresses in the pavement concrete70


AUTUMN :2012-2013

Modulus of elasticity of concrete & poissons ratio of concrete

Following values were adopted for stress analysis for the concrete

with 28 day flexural strength of 4.5 Mpa (4.95 MPA for 90 day strength)

E = 30,000 Mpa = 0.1571


AUTUMN :2012-2013

(ii) Coefficient of Thermal expansion ()

It is dependent to a great extent on the type of aggregates used in concrete However, for design purpose, a value of

= 10 x 10-6 per 0C is adopted

72


AUTUMN :2012-2013

(iii) Fatigue Behavior of Cement Concrete

Due to repeated application of flexural stresses by the traffic loads - progressive fatigue damage takes place in the cement concrete slab in the form of gradual development of micro-cracks especially when ratio between the applied flexural stress and the flexural strength of concrete is high. This ratio is termed as stress ratio (SR)73


AUTUMN :2012-2013


If the SR is less than 0.45, the concrete is expected to sustain infinite number of repetitions

As the stress ratio increases, the number of load repetitions required to cause cracking decreases.

74


AUTUMN :2012-2013


The relation b/w fatigue life (N) and stress ratio is given in Eqns below:

N = unlimited for SR < 0.45

N = 4.2577SR-0.43253.268When 0.45 SR 0.55 ------- (6)75


AUTUMN :2012-2013


log10 N =

0.08280.9718- SRFor SR > 0.55 ------ (7)These fatigue criteria's are used for checking the adequacy of the pavement slab on the basis of Miners hypothesis

It is assumed that the fatigue resistance not consumed by repetitions of one load is available for repetitions of other loads 76

Design of slab thicknesstransportation ENGINEERING GROUPDEPARTMENT OF CIVIL ENGINEERINGINDIAN INSTITUTE OF TECHNOLOGY ROORKEEROORKEE 247 667, Uttarakhand, INDIA

AUTUMN :2012-2013

Critical Stress Condition

The flexural stress due to the combined action of traffic loads and temperature differential b/w top and bottom fibers of the concrete slab is considered for design of pavement thickness

The effect of moisture change is opposite to that of temperature change and is not normally considered critical to thickness design 77


AUTUMN :2012-2013

Critical Stress Condition The flexural stress at the bottom layer of the concrete slab is the maximum during the day hours when the axle loads act midway on the pavement slab while there is a positive temperature gradient as shown in Fig.1. This condition is likely to produce bottom up cracking (BUC)

Fig. 1. Axle Load Placed in the Middle of the Slab during Mid-Day78


AUTUMN :2012-2013

Critical Stress Condition During the night hours, the top surface is cooler than the bottom surface and the ends of the slab curl up resulting in loss of support for the slab as shown in Fig.2. Fig. 2. Two Axles of CV on a slab curled during night hours

Due to the restraint provided by the self weight of concrete and by the dowel connections, temperature tensile stresses are caused at the top79


AUTUMN :2012-2013

Critical Stress Condition Fig. 2 shows the placement of axle loads close to transverse joints when there is negative temperature gradient during night period causing high flexural Fig. 2. Two Axles of CV on a slab curled during night hours

stresses in the top layer leading to top-down cracking (TDC)80


AUTUMN :2012-2013

Locations of points of maximum flexural stress at the bottom of the pavement slab without tied concrete shoulder for single, tandem and tridem axles are shown in Fig.Fig. 2. Two Axles of CV on a slab curled during night hours The tyre imprints are tangential to the longitudinal edge.

81Placement of Axles for Maximum Edge Flexural stress at Bottom of the slab without Tied Concrete Shoulders


AUTUMN :2012-2013

For the tied concrete shoulders also, the maximum stress occurs at the same locations82


AUTUMN :2012-2013

Different axle load positions causing tensile stress at the top of the slab with tied shoulder Shoulder83


AUTUMN :2012-2013

Single axles cause highest stress followed by tandem and tridem axles respectively.

Spacing between individual axles for tandem and tridem axles varies from 1.30 m to about 1.40m.

There is practically no difference in stresses for axle spacing b/w 1.30m and 1.40m.

A spacing of 1.30m can be taken for stress calculation84


AUTUMN :2012-2013

For analysis of bottom up cracking

Pavement with tied concrete shoulders for single rear axlePavement without concrete shoulders for single rear axlePlacement with tied concrete shoulders for tandem rear axlePavement without concrete shoulders for tandem rear axle85


AUTUMN :2012-2013

For analysis of Top-down cracking

Pavements with and without dowel bars having front steering axle with single tyres and the first axle of the rear axle unit (single/tandem/tridem) placed on the same panel as depicted below

86


AUTUMN :2012-2013

For heavy traffic conditions, dowel bars are usually provided across transverse joints for load transfer

Tied concrete shoulders are also necessary for high volume roads

However, for smaller traffic volumes smaller than 450 CV/day,

No tied concrete shoulders and dowel bars warranted87


AUTUMN :2012-2013

Terminal load transfer efficiencies (LTE) for

dowelled transverse joints = 50%

and tied joints between the slab and concrete shoulder = 40% for stress computation

But as per Mechanistic-Emperical Pavement Design Guide (NCHRP, 2004) these values are 60% & 50% respectively for dowelled joints and tied joints b/w slab and conc shoulder

Considered in the present design of IRC:58-2011National Cooperative Highway Research Program (NCHRP)88


AUTUMN :2012-2013

CUMULATIVE FATIGUE DAMAGE ANALYSIS (CFD)

For a given slab thickness and other design parameters, the pavement will be checked for cumulative bottom-up and top-down fatigue damage

For bottom-up cracking, the flexural stress at the edge due to combined action of single or tandem rear axle load and positive temperature differential cycles is considered89


AUTUMN :2012-2013

CUMULATIVE FATIGUE DAMAGE ANALYSIS (CFD)

The flexural stress is divided by the design flexural strength (modulus of rupture) of the cement concrete to obtain stress ratio (SR)

If the stress ratio is less than 0.45, the allowable no. of cycles of axle load is infinity

If the stress (SR) is values greater than 0.45, allowable cycles of loading (axle + temperature) can be estimated using Eqns. 6 & 790


AUTUMN :2012-2013

The cumulative fatigue damage caused to the slab during its service life should be equal to or less than one

CFD for bottom-up cracking is significant only during 10 AM to 4 PM (Six hours)

Because of higher stresses due to simultaneous action of wheel load and positive temperature gradient

Thus, the day hour traffic during the six hour is to be considered for BUC91


AUTUMN :2012-2013

For top-down cracking analysis, only the CFD caused during the period

between 0 AM and 6 AM is important

If the exact proportions of traffic expected during the specified six-hour periods are not available, it may be assumed that

the total night time traffic is equally distributed among the twelve night hours92


AUTUMN :2012-2013

Similarly, the total day time traffic is equally distributed uniformly among the twelve day hours

The cumulative fatigue damage (CFD) expression for bottom-up and top-down cracking cases are given by eqns 8 & 9

CFD (BUC) =

CFD (TDC) =

JiniNi( 10 AM to 4 PM) ----- (8)JiniNi( 0 AM to 6 AM) ----- (9)93


AUTUMN :2012-2013

Ni = Allowable number of load and temperature differential cycles for the wheel load group the specified six hour period

n i = predicted number of load and temperature differential cycles for the ith load group during the specified six-hour period

J = total number of load groups

94


AUTUMN :2012-2013

Radius of relative stiffness ()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 layer depends both on relative stiffness of the pavement slab with respect to that of sub-grade.95


AUTUMN :2012-2013

Radius of relative stiffness ()Westergaard defined this by a term "Radius of relative stiffness" which, can be written numerically as below: l = [Eh3/ (12K(1-2)]0.25

Where, l = radius of relative stiffness, cm E = Modulus of elasticity of cement concrete kg/cm2 U = Poisson's ratio for concrete = 0.15 K = Modulus of Sub-grade reaction in kg/cm2

96


AUTUMN :2012-2013

Equivalent Radius of Resisting section (b):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.Numerically, b= (1.6.a2 + h2)0.5 - 0.675.hHere, 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, cmWhen 'a' is greater than 1.724.h, b =a.97


AUTUMN :2012-2013

Equivalent Radius of Resisting section (b):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)0.5Here, 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.98


AUTUMN :2012-2013

99

Flexible

Documents

Transcript of Flexible