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In this article we will discuss about how to design plain jointed rigid pavements for highways by IRC Method.

**IRC Method of Rigid Pavement Design****: **

This method is based on mechanistic-empirical principles and the use of software IITRIGID for the computation of flexural stresses due to single and tandem axle loads.

**The design of a rigid pavement consists of: **

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(i) Determination of the thickness of pavements;

(ii) The design of joints; and,

(iii) The design of load-transfer devices such as dowel bars and tie bars.

**Determination of the Thickness of Pavement Slab****: **

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**The following steps may be used for this purpose: **

1. Assume a trial thickness for the slab.

2. Calculate the stresses due to load [σ_{e} and σ_{c} from Eq. 7.23 and 7.24] and those due to warping (σ_{txi}, σ_{tyi} , σ_{ txe} and σ_{tye} from Eqs. 7.27 to 7.30)

3. Calculate the stress ratio (SR) by dividing the edge stress due to load by the flexural strength of the concrete (modulus of rupture, MR)

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4. Obtain the expected number of standard axle load repetitions (N) for each stress ratio by the following standard relations for each group of axle loads (or fatigue life, N_{f}):

5. Calculate the cumulative fatigue damage developed by different groups of axle load and sum up.

6. The summed up value of the cumulative fatigue damage for all the expected axle loads should not exceed unity. If this criterion is satisfied, proceed to the later steps. The adequacy of flexural strength of the slab has to be checked for- (i) total maximum stress at the edge due to wheel load and warping, and (ii) maximum stress at the corner due to wheel load. The trial thickness is considered adequate if the maximum stresses are less than the modulus of rupture of the concrete.

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If these criteria are not satisfied, revise the thickness upwards and follow the same procedure again to ensure the adequacy of the slab thickness. (Warping stress at the corner is not considered as it is less than the stresses in the other locations of the slab. Also, the effect of moisture changes is ignored.)

Stress at the edge due to wheel load may be determined from either Eq. (7.23) or from charts developed by IRC for different axle loads. Single axle loads of 60 KN to 240 KN and tandem axle configurations from 120 KN to 440 KN, and incorporated in their guidelines (IRC: 58-2002). Warping stress at the edge is calculated using Eqs. (7.29) and (7.30).Two typical charts are shown – one for a single axle load of 160 KN and another for tandem axle load of 360 KN. [Fig. 7.19 (a) and (b)].

**The modulus of subgrade reaction, k (Kg/cm ^{3}), may be got from CBR percent as shown below (IRC: 58-2002): **

**The design procedure for the pavement thickness using IRC guidelines (IRC: 58-2002) is given below in the form of flow-chart for convenience (Fig. 7.20): **

**Low Traffic-Volume Rigid Pavements for Rural Roads (IRC: SP: 62-2004): **

Using the guidelines contained in IRC: SP: 62-2004, the thickness of the pavement for low traffic-volume rural roads may be determined.

**The salient features of the method are given below: **

(i) The minimum wheel load considered is 30 kN, with a minimum tyre pressure of 0.5 Mpa. If the traffic consists of mini-trucks/buses, the wheel load should be taken as 51 kN with a tyre pressure of 0.7 MPa.

(ii) K-value for the subgrade may be got from plate load tests or from CBR, through correlation.

(iii) For a design wheel load of 51 KN, a 150 mm-thick WBM subgrade is provided. For a wheel load of 31 kN, a sub-base of 75 mm thickness (WBM) is provided. In both cases K-value for subgrade is increased by 20%.

(iv) A design life of 20 years is recommended based on past experience.

(v) The design value of flexural strength of concrete is considered as that after 90 days (or about 1.2 times 28-day strength). No heavy traffic is allowed for the first 90 days.

(vi) Fly ash can be used as partial replacement up to 35%.

(vii) Ec is taken as 3 x 104 MPa, ϒ as 0.15, and a as 10 x 10-6/°C.

(viii) The cement concrete should conform to “IRC: 44-2008.”

(ix) For very low traffic, a single lane of 3.0 m to 3.75 m without longitudinal joints may be used.

(x) At expansion joints of 20 mm width, dowel bars of 25 mm across and 500 mm long are used at 250 mm intervals.

(xi) Only stresses due to wheel load and warping are considered for thickness design. Wheel load repetitions and fatigue consumption value need not be considered.

(xii) Edge stresses due to wheel load and corner stress can be got from Eqs. (7.23) and (7.24) respectively. Edge warping stress can be got using Eqs. (7.29) and (7.30). Wheel contact

area is taken to be circular with radius a, which is got as α = (W/πp)^{0.5}.

**Design of Reinforcements for Pavement Slab****: **

Guidelines for the design of reinforcements in a concrete pavement are given here. (It must be remembered that their function is to control the occurrence of cracks). In addition, it counteracts the tensile force due to shrinkage and contraction due to temperature as well as moisture changes.

(i) The maximum tension in the steel across the crack is the force needed to overcome friction between the slab and the layers below, from the crack to the nearest joint and free edge.

(ii) Maximum force occurs for a crack at the mid-span of the slab; therefore, the greater the spacing of joints, the greater is the required reinforcement.

(iii) Major portion of the reinforcement should be parallel to the greater dimension.

The following formula is popularly used for the area, A_{s}, in cm^{2}, of the longitudinal and transverse steel per metre width or length of the slab-

Here,

L_{j} = Spacing in metres between transverse joints (for longitudinal joints), or free longitudinal joints (for transverse steel).

ƒ = coefficient of friction between slab and subgrade (usually, maximum 1.5)

h = thickness of slab in metres

ϒ_{c} = unit weight of concrete (kg/m^{3}, usually 2400)

σ_{s} = allowable stress in steel in kg/cm^{2} (Usually taken as 50 to 60% of yield stress-1400).

The steel in the slab is placed about 50 mm below the top surface since greater tensile stresses are expected near the top, where the cracks tend to open. (IRC: 58-2002)

**Joints in Cement Concrete Pavements****: **

It has been seen that stresses are caused in pavements, besides those due to wheel loads, by changes in temperature and moisture and shrinkage or contraction during setting. Long slabs are bound to crack heavily owing to these factors.

Hence there is a need to limit the dimensions of the slab by dividing it into smaller units by interposing joints. The joints will ensure that the stresses due to expansion, contraction and warping are within limits. The longer the slab is, the greater the warping stresses and the larger the reinforcements needed.

This is the basic reason to provide joints in cement concrete pavements.

**Types of Joints: **

**Based on their function, joints in cement concrete pavements are classified as given below: **

(a) Expansion joints

(b) Contraction joints

(c) Warping joints

(d) Longitudinal joints

(e) Construction joints

**The general requirements of all types of joints are: **

1. The joint must not impose any resistance on the slab movements.

2. The joint must be sealed properly to exclude water and dust

3. The joint should not affect the riding quality of the pavement.

4. The joint should not cause any hindrance in laying the concrete.

5. The structural strength of the slab should not be affected by the joint.

The design of joints should be such that it facilitates efficient transfer of load from one slab to the adjacent one.

**(a) Expansion Joints: **

These are intended to provide space in the pavement for expansion of the slab, which occurs when the temperature rises. Expansion joints also reduce the stresses caused by contraction and warping. However, expansion joints are altogether omitted in modern design practice since the function of these joints is fulfilled by the other types of joints designed in the pavement. A typical expansion joint is shown in Fig. 7.21.

The expansion gap is usually 20 mm, in which a compressible joint filter is interposed. A sealing compound is used near the surface in the gap. The dowel bar is a load-transfer device – from one slab to the adjacent one; a thin coating of bitumen on the surface of the dowel bar breaks the bond with concrete, thereby permitting expansion.

**(b) Contraction Joints: **

Contraction of the slab occurs when the temperature falls (compared to the laying temperature), which induces tensile stresses, resulting in cracking of the slab. Joints provided in the transverse direction to eliminate cracks by counteracting the tensile stresses, are called contraction joints.

A popular form of contraction joint is groove joint, also called a dummy joint. The salient features are a surface groove (formed by a flat metal plate driven when the concrete is green), a sealing compound to fill this groove, and a dowel bar to act as a load-transfer device. The slab cracks at the location below the groove; warping stresses are also relieved to some extent. A typical dummy contraction joint is shown in Fig. 7.22.

**(c) Warping Joints: **

These are also known as hinge joints, intended to relieve warping stresses. Warping joints can be either in the transverse direction or in the longitudinal direction. They permit hinge action but do not allow appreciable separation of the adjacent slabs.

This is the primary difference between the warping joints and the other types. To achieve the primary purpose of these joints, reinforcements are continued through the joints, or tie-bars are provided across them. A typical tongue-and-groove type of longitudinal warping joint is shown Fig. 7.23.

**(d) Longitudinal Joints: **

A longitudinal joint is provided when the width of the pavement is more than 5 m, to facilitate construction in strips. This type of joint allows for warping and takes care of uneven settlement of the subgrade. To achieve this, some form of load- transfer device becomes necessary; usually, fully bonded tie-bars (12.5 mm to 25 mm diameter, and 1 metre long) with 600 mm centre-to-centre spacing are provided to serve this purpose.

Alternatively, a tongue-and-groove joint (Fig. 7.23) may also be provided.

A typical butt-type longitudinal joint with tie-bar is shown in Fig. 7.24.

**(e) Construction Joints: **

This type of joint becomes necessary when the slab-laying work has to be stopped for the day at a point, where there would be otherwise no joint. With proper planning, a day’s work may be stopped at an expansion joint or a contraction joint. The reinforcements should be continued across the joint. A groove near the surface, filled with a sealing compound, arrests the entry of water and dust.

**Spacing of Joints: **

This is governed by the number of factors; such as temperature gradient, slab thickness, and the amount of reinforcing steel provided. The joint spacing can be from 7.5 to 25 m, making every third or fourth joint an expansion joint. The other joints are made contraction joints.

**The joint spacing recommended by “IRC: 58-2002” is given in Table 7.16: **

**Details of Joints used in Two-Lane Pavement:**

Based on the above discussion the details of joints used in a two-lane cement concrete pavement are shown pictorially in plan in Fig. 7.25.

**Design of Spacing of Joints****: **

Different criteria govern the spacing of the various types of joints provided in cement concrete pavements used for highways.

**Spacing of Expansion Joints: **

The spacing of expansion joints is governed by the gap or width of the joint and the maximum temperature differential in the region. This spacing is also adjusted such that contraction joints are equally spaced.

The width of the joint depends also on the free length of the slab. The greater the spacing, the longer the width required as the gap to allow for expansion. However, this gap should not be too high as it widens during winter; also, the dowel bars at the joint will be subjected to high bending and bearing stresses if the gap is large. Hence, the IRC recommends a maximum gap of 25 mm.

Let the length of the slab be L_{e} and let it expand by δ for a temperature differential, Δt. If α is the coefficient of thermal expansion of concrete per degree temperature change,

Δ = L_{e}.α.Δt

The joint filter may be assumed to be compressed up to 50% of its thickness; so, the expansion gap should be 2δ. Hence, if δ is half the expansion gap or joint width, e, the spacing of the expansion joint, L_{e} is given by-

**Spacing of Contraction Joints****: **

Contraction joint spacing is governed by the anticipated frictional resistance and the allowable tensile stress in concrete during the curing period, or the amount of steel reinforcement, if provided.

The slab contracts during winter when the temperature falls below the laying temperature, and also due to shrinkage of cement concrete during the curing period. This movement is resisted by the frictional force between the slab and the subgrade (Fig. 7.26).

Total frictional force for a distance (L_{c}/2)

In this equation,

σ_{t} = allowable tensile stress in concrete (kg/cm^{2}, usually 0.8)

ϒ_{c} = unit weight of concrete (kg/m^{3}, usually 2400)

ƒ = coefficient of friction (usually not more than 1.5)

b = width of the slab (m)

h = thickness of the slab (cm)

Then, the spacing L_{c}, will be obtained in metres.

**Reinforced Cement Concrete Slabs: **

If it is assumed that the reinforcing steel takes the entire tensile force caused by the frictional forces from the subgrade and ‘hair cracks’ are allowed in concrete,

In this equation,

σ_{s} = allowable tensile stress in steel (kg/cm^{2}, usually 1400)

A_{s} = total area of steel (cm^{2}) across the width of slab

b = slab width (m)

h = slab thickness (cm)

ϒ_{c} = unit weight of concrete (kg/m^{3}, usually 2400)

ƒ = coefficient of friction (maximum 1.5).

Thus, the spacing, L_{c}, will be obtained in metres.

**Design of Dowel Bars: **

IRC recommends the following procedure for determining the load transfer capacity of a single dowel bar (IRC: 58-2002)-

The effective length of dowel bar for load transfer on either side of the load position is taken to be 1.8l, l being the radius of relative stiffness.

Assuming linear variation of the capacity factor from 1.0 under the load to zero at a distance 1.8l from it, the capacity factors for the dowel system are calculated for different spacings. The spacing which corresponds to the required capacity factor, n, is chosen.

Generally, the diameter of dowel bar is 25 mm and the length is 500 mm. The spacing is 200 mm for 150 mm-thick slab and 300 mm for 200mm-thick slab, according to IRC recommendations.

**Design of Tie-Bars: **

Where,

b = Distance between the joint and the nearest free edge (metres)

f = Coefficient of friction between pavement and subgrade (taken usually as 1.5)

ϒ_{c }= Unit weight of concrete (kg/m^{3})

h = Thickness of pavement slab (m)

σ = Allowable working stress in steel (kg/cm^{2})

The maximum diameter of tie-bars is limited to 20 mm to allow warping. The maximum spacing is 75 cm. The calculated length of the tie-bar, L_{t}, is increased by 5 to 8 cm to allow for any inaccuracies in placing.

* All the allowable stresses in concrete and steel have to be in accordance with Indian Standard Code of Practice- “IS: 456-2000: Indian standard plain and reinforced concrete – Code of practice (Fourth Revision)”, Bureau of Indian Standards, New Delhi, 2000.

**IRC: 58-2011 – Guidelines for the Design of Plain Jointed Rigid Pavements for Highways (Third Revision)****: **

The IRC have brought out these revised guidelines for the design of plain jointed cement concrete pavements, with and without tied concrete shoulders, for an average daily commercial traffic volume of more than 450 (vehicles with laden weight exceeding 3 tonnes). [IRC: SP: 62 may be referred to for the design of low-volume rural roads.] ~~ ~~

These guidelines include the spectrum of axle loads of vehicles with tandem axles, tridem axles, and multiple axles. The concept of cumulative fatigue damage due to the combined effect of load and pavement temperature variations, introduced in the previous version – IRC: 58-2002 (Second Revision) continues to be adopted in this revised version also.

These guidelines also include a procedure for the design of pavements with widened outer lane, tied concrete shoulder, pavements bonded to cemented sub-base, design of longitudinal joints, and expansion and contraction joints.

**The salient features are: **

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

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

(iii) Design for top-down fatigue cracking caused by single, tandem and tridem axle load applications.

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

(v) Design guidelines for pavements without concrete shoulders and with tied concrete shoulders.

(vi) Consideration of concrete slabs with unbonded as well as bonded cement-bound sub- base.

**Types of Concrete Pavements****: **

Several types of concrete pavements have been used; typical cross-sections of the pavements are shown in Fig. 7.27 where

PQC- Pavement quality concrete; DLC: Dry lean concrete; BC: Bituminous concrete; DBM: Dense bituminous macadam

**Factors Governing Design of Concrete Pavements: **

1. Design period

2. Commercial traffic volume and their directional distribution

3. Composition in terms of single, tandem, tridem and multi-axles

4. Axle-load spectrum

5. Tyre pressures

6. Composition and strength of foundation

7. Climatic considerations

**Axle Loads:**

**Legal axle-load limits in India are:**

Single axle – 100 KN

Tandem axle – 186 KN

Tridem axle – 235 KN

Data on axle-load spectrum is required to estimate the repetitions of single, tandem and tridem axles in each direction expected during the design period.

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

**Tyre Pressures:**

The range of tyre inflation pressures of commercial vehicles is 0.7 MPa to 1.0 MPa. A tyre pressure of 0.8 MPa is adopted for design. (When the thickness of pavement is more than 200 mm, stresses on the pavement are not affected significantly by the variation of tyre pressure.)

**Design Period:**

Cement concrete pavements may be designed for a life span of 30 years or more. However, the design engineer should use his judgment about this, based on the various factors associated with the particular project.

**Design Lane: **

The lane carrying the maximum number of heavy commercial vehicles is termed as the 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.

**Temperature Differential: **

The temperature differential between the top and bottom fibres of concrete pavements causes the slab to curl, giving rise to stresses. The variation between the top and the bottom is non-linear during the day and nearly linear during the night. The maximum differential during the night is nearly half that during the day; this varies somewhat with slab thickness. Temperature differential is positive during the day when the slab tends to have a convex shape, and it is negative during the night when it tends to have a concave shape.

CBR of soil below the select 500 mm subgrade should be determined for calculating the effective CBR of the subgrade and its k value for suitable design of the concrete pavement. A minimum subgrade CBR of 8% is recommended.

**Representative k-values for different CBR-values are given below: **

28-day flexural strength of pavement quality concrete should not to be less than 4.5 MPa. Modulus of elasticity, E = 30,000 MPa

Poisson’s ratio, μ = 0.15

Coefficient of thermal expansion, α = 10 x 10^{-6}/°C

**Fatigue Behaviour of Concrete:**

The relationships between fatigue life, N, and the stress ratio, SR, given in the 2002-version of the guidelines are applicable.

The flexural stress due to combined action traffic loads and temperature differential between the top and bottom fibres of the slab is considered for the design of pavement thickness. The flexural stress at the bottom layer of the slab is the maximum during the day when the axle loads act midway on the pavement slab; this condition is likely to produce ‘bottom-up cracking’. During the night, the negative temperature differential coupled with axle loads placed close to transverse joints initiates ‘top-down cracking’.

**Calculations of Flexural Stress: **

The IITRIGID software used in the previous version of IRC: 58 (that is, of 2002) is valid for the computation of load stress in the edge region of the pavements without tied concrete shoulders if there is no temperature gradient in the slab.

Finite Element Method (FEM) is more appropriate for stress computation for a wide variety of load, temperature, geometry and boundary conditions. Finite element analysis is carried out using IITSLAB-II, a software developed at IIT Kharagpur, to compute flexural stress due to the combined action of load (single, tandem and tridem axles) and different temperature differentials (positive and negative).

It has been observed that, for zero temperature differential, flexural stresses decrease with increase in k values for all thicknesses. If there is a positive temperature differential, the warping stresses are high for thicker slabs and it results in higher flexural stresses in slabs for higher k values. For a thickness of about 270 mm, the modulus of subgrade reaction has practically no effect on flexural stresses. Thus, increasing the k value does not help in thickness design due to high curling stresses caused by a stiff support.

For cases where the slabs crack bottom-up, the combination of load and positive non-linear temperature differential has been considered; whereas for top-down cracking analysis, the combination of load and negative linear temperature differential has been taken. For each case, the critical load positions in the case of different types of axle loads – single, tandem, tridem and multi-axle – are considered for producing the maximum edge stress.

**Analysis has been done for the following cases: **

1. Pavement with tied concrete shoulders for single rear axle.

2. Pavement without concrete shoulders for single rear axle.

3. Pavement with tied concrete shoulders for tandem rear axle.

4. Pavement without concrete shoulders for tandem rear axle.

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 the pavement slab.

The result of finite element analysis of a large number of concrete pavements with different pavement configurations subjected to various combinations of axle loads and temperature differentials have been presented in the form of charts – for edge flexural stress. Linear interpolation can be done for intermediate loads and temperature from the charts.

Analysis of the results has also been used to develop regression equations for estimation of the flexural tensile stress in the slab for different pavement types for bottom-up as well as top-down cracking cases.

**Tied Concrete Shoulder and Widened Outer Lane: **

These are recommended to protect the edge of high traffic volume highway pavements. The widening could be 0.5 to 0.6 m. The edge stress is reduced to the extent of 20 to 30%, which results in the reduction of pavement thickness.

**Design Procedure: **

The general design procedure is practically similar to the trial-and-error approach given in the 2002 guidelines. A trial thickness is assumed, critical stresses are computed, and compared with the concrete strength values. If necessary, the procedure is repeated with increased slab thickness until a satisfactory thickness is found.

**Continuously Reinforced Cement Concrete Pavements (CRCP): **

Of late, concrete pavements are being constructed with continuous reinforcement, eliminating the transverse joints; of course, this requires the provision of adequate reinforcements.

CRCP slabs develop numerous fine transverse cracks. However, they appear only at the surface and hence do not affect the structural performance.

CRCP slabs do require heavy reinforcements (generally not less than 55t/m^{2}). Longitudinal reinforcement is not less than 0.60% of the cross-sectional area, consisting of deformed bars placed at 1/3 to 1/2 the slab depth. Tied to the longitudinal bars, are transverse reinforcement of deformed steel bars over the entire width.

The area of steel is calculated from Eq. (7.33). CRC pavements are used for very heavy traffic and are much more expensive than ordinary reinforced cement concrete slabs with joints. If necessary, a relatively thin bituminous surfacing may be provided over CRCP.

**Recent developments in Cement Concrete Pavement Design: **

There are a few recent developments in the design and use of cement concrete for rigid pavements.

**These are listed below: **

1. The concept of reliability based on probabilistic approach.

2. The concept of serviceability and serviceability index and its loss during design life of a pavement.

3. The concept of fatigue, fatigue life and fatigue life consumed through repetitions of axle loads in the design of rigid pavements.

These concepts were introduced by the AASHTO (1993) and have been adopted by the IRC. An exhaustive treatment of the IRC Guidelines has already been given, and the principles of design based on these guidelines will be better appreciated after going through the relevant Numerical Examples.

**Pre-Stressed Concrete Pavements (PSC): **

The principle of pre-stressing enhances the tensile strength of concrete by inducing compressive stresses in it initially. The load-carrying capacity is thus greatly increased. Joint spacing also can be far more than in plain concrete pavements. The thickness of slab also gets reduced, and the riding quality of the surface is improved.

However, the availability of expertise, the need for enhanced capacity, and the resources to meet the additional cost are the governing criteria for their use.

Fibre-reinforced concrete (FRC) is a recent technique. It differs from RCC and PSC in that the amount and location of the reinforcement are not governed by loading conditions and the tensile stresses. The fibres are of steel, polypropylene, polyethylene or nylon, and are dispersed randomly in short lengths. This improves the structural quality of the concrete pavement uniformly.

FRC has a crack-arresting mechanism and improves both the tensile strength and fatigue resistance of cement concrete.

In highway pavements, these qualities are considered to be extremely valuable. Once again, the need, the availability of materials and expertise and the financial resources govern the choice of FRC for highway pavements.