BITUMINOUS MATERIALS
RIGID PAVEMENT DESIGN CONTENTS :
TRANSPORTATION ENGINEERING UNIT - 10
RIGID PAVEMENT DESIGN CONTENTS :
Aims / Objectives 10.1. Introduction
10.2. Stresses due to Loading
10.3. Stresses due to changes in Temperature 10.4. Combination of Stresses
10.5. IRC Recommendations 10.6. Joints in Concrete Pavements
10.7. Self-assessment Questions 10.8. Summary
10.9. References AIMS / OBJECTIVES :
Stresses are set up in concrete road slab by loading, by changes in temperature and moisture content and by other causes. Methods of calculation of these stresses and the design principles of concrete road slabs based on the IRC recommendations are presented. Joints are provided in concrete pavements to allow for movements of the slabs due to changes in temperature and moisture content. Considerations for the spacing of these joints are also discussed.
10.1. INTRODUCTION :
Stresses are set up in a concrete road slab by loading, by changes in temperature and moisture content, and other causes. The worst combination of stress - producing failure conditions have to be considered for design of these slabs. Since concrete is very much weaker in tension than in compression, only maximum tensile stresses need be considered.
As such cement concrete pavement should be designed and controlled on the basis of flexural strength of concrete of 4000 KN / m2(40 kg / cm2).
The stresses due to loads and due to changes in temperature are of the same order of magnitude and are considerably grater than those due to changes in moisture content. The stresses caused by the resistance of the sub-grade to expansion and contraction produced by change in temperature and moisture content are relatively smaller in short slabs, but may be more important in long slabs. The stresses caused by dilatency of the sub-grade are small and need not usually be considered.
Joints are provided in concrete roads to allow for expansion, contraction and warping of the slabs caused by the changes in the temperature and moisture content of the concrete.
They are also necessary to allow for the break in construction at the end of days work and to allow the road to be laid in lanes of convenient width. The number of joints should be kept to a minimum compatible with the above requirements, because the construction of joints involves a considerable amount of extra work and is liable to interfere with smooth progress of concreting. The design of various types of joints is also considered.
10.2. STRESSES DUE TO LOADING :
Several theories have been developed on the occurrence of stresses in concrete slabs resting on a uniform bed. The most commonly used method of calculation of the stresses in a slab is due to Westergaurd. The theory applies to slabs of finite extent, and expressions are derived for stresses due to loading at the interior, edges and corners of the slabs. Westergaurd assumed that the concrete slab is homogeneous and has uniform elastic properties, and that the reaction of the sub-grade (p) is vertical and proportional to the deflection ( ). In other words he assumed that the support given to the slab is similar to that given by a dense fluid and hence that the sub-grade has no shear strength. Then according to Westergaurds assumption p = K where K is defined as the ‘modulus of sub-grade reaction’. The modulus of sub-grade reaction is also referred to as ‘Spring constant’ and as the ‘dense liquid constant’. The modulus of sub-grade reaction is determined by means of the plate load test using a plate of 75 cm dia or square. The modules of sub-grade is the stress per unit deflection and the units are KN/m3(Kg/cm3).
10.2.1. Critical Load Positions :
Westergaurd considered stresses produced by three conditions of loading (i) loading at positions away from the edges (interior loading) (ii) loading at the edges (but away from the corners) and (iii) loading at the corners. These positions are shown in Fig. 10.1.
Westergaard also assumed that the wheel load is uniformly distributed over a circular area of contact in the case of interior and corner loading and over a semi-circular area of contact in the case of edge loading. The position and direction of the tensile stresses for each of critical positions of the loading are as follows.
a) Loading at the interior - at the bottom of the slab and of the same magnitude in all directions.
b) Loading at the edge-at the bottom on the slab parallel to the edge. (Another smaller tensile stress will occur at the top of the slab at right angles to the edge).
c) Loading at the corner - at the top of the slab parallel to the bisector of the corner angle.
Fig. 10.1. Critical Load Position The stress equations given by Wester-gaurd are as follows.
a) Interior Loading :
Si= 0.316 P / h2(4 log10 (l / b) + 1.069) 10.1 b) Edge Loading :
Se= 0.572 P / h2(4 log10 (l / b) + 0.359) 10.2 c) Corner Loading :
Sc= 3 / h2
6 .
/ 0
1 2
l c
a 10.3
Here,
Si, Se and Sc = maximum stress for interior, edge and corner loading, respectively, kg/cm2.
h = slab thickness, cm P = wheel load, kg
a = radius of contact area (wheel load distribution) cm.
l = radius of relative stiffness, cm.
b = radius of resisting section, cm.
The terms radius of relative stiffness and radius of resisting section are explained below.
Radius of Relative Stiffness - The pressure deformation characteristics of a cement concrete slab is a function of the relative stiffness of slab to that of the sub-grade. According to Wester gaard the radius of relative stiffness is given by the following equation :
l =
(
Eh)
k3 4 2
12 1 µ 10.4
Equivalent radius of Resisting Section - Considering the positions of interior loading and edge loading, the maximum bending moment occurs at the loaded area and acts radially in all directions. With the load concentrated on a small area of the pavement the question arises as to the sectional area of the pavement, that is effective in resisting the bending moment. According to Wester gaard, the equivalent radius of resisting section is approximated, in terms of radius of load distribution and slab thickness as follows.
b = 1.6 a2 +h2 0.675 h when a / h ! 1.724 10.5 where E = Modulus of Elasticity of concrete, Kg / cm2
µ= Poissons ratio of concrete,
k = Modulus of sub - grade reaction - Kg / cm3 Other terms have been already defined.
When a/h > 1.724, b = a.
10.2.2. GOLD BECK’S FORMULA :
Gold beck indicated that many concrete slabs failed at the corners. Gold beck’s formula for stress due to corner load is given by
Sc = 3 P / h2
10.2.3. BRAD BURY’S EQUATION :
Brad bury assumed partial sub-grade support of the pavement slab at the edges and gave the following empirical equation based on the use of Westergaard’s theory.
" = (P / h2) Q here " = Stress, kg/cm2
P = Wheel load, kg
Q = Brad bury’s stress coefficient.
The value of stress coefficient, Q is determined by the ratio of 1/b in the case of interior and edge loading and by the ratio of a / 1 in the case of corner loading. These values may be used for calculating the wheel load stresses.
The stress coefficients Qi and Qe for interior and edge loading are given in Table 10.1 for various values of l/b. The values of Qc for corner loading are given in Table 10.2.
10.2.4. FORMULAE RECOMMENDED BY THE I.R.C. :
The I.R.C. recommends the following two formulae for analysis of load stresses at the edge and corner regions and for the design of rigid pavements.
1. Load stress Se in critical edge region.
Se - 0.529 P/h2(1+0.54µ) (4 log10(l/b) + log10b - 0.4048) 10.8 (This is Wester gaard’s Equation modified by Teller and Sutherland).
ii. For load stress Sc at the critical corner region.
Sc = 3 P / h2 1
(
a 2 1/)
1 2. 10.9(This is Wester gaard’s equation modified by Kelley) Various terms have already been defined.