Note for Highway and Traffic Engineering - HTE by Gurpreet Mains
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CHAPTER 29. RIGID PAVEMENT DESIGN NPTEL May 7, 2007 Chapter 29 Rigid pavement design 29.1 Overview As the name implies, rigid pavements are rigid i.e, they do not flex much under loading like flexible pavements. They are constructed using cement concrete. In this case, the load carrying capacity is mainly due to the rigidity ad high modulus of elasticity of the slab (slab action). H. M. Westergaard is considered the pioneer in providing the rational treatment of the rigid pavement analysis. 29.1.1 Modulus of sub-grade reaction Westergaard considered the rigid pavement slab as a thin elastic plate resting on soil sub-grade, which is assumed as a dense liquid. The upward reaction is assumed to be proportional to the deflection. Base on this assumption, p where ∆ is the displacement Westergaard defined a modulus of sub-grade reaction K in kg/cm3 given by K = ∆ level taken as 0.125 cm and p is the pressure sustained by the rigid plate of 75 cm diameter at a deflection of 0.125 cm. 29.1.2 Relative stiffness of slab to sub-grade A certain degree of resistance to slab deflection is offered by the sub-grade. The sub-grade deformation is same as the slab deflection. Hence the slab deflection is direct measurement of the magnitude of the sub-grade pressure. This pressure deformation characteristics of rigid pavement lead Westergaard to the define the term radius of relative stiffness l in cm is given by the equation 29.1. s Eh3 l= 4 (29.1) 12K(1 − µ2 ) where E is the modulus of elasticity of cement concrete in kg/cm2 (3.0×105), µ is the Poisson’s ratio of concrete (0.15), h is the slab thickness in cm and K is the modulus of sub-grade reaction. 29.1.3 Critical load positions Since the pavement slab has finite length and width, either the character or the intensity of maximum stress induced by the application of a given traffic load is dependent on the location of the load on the pavement surface. There are three typical locations namely the interior, edge and corner, where differing conditions of slab continuity exist. These locations are termed as critical load positions. Introduction to Transportation Engineering 29.1 Tom V. Mathew and K V Krishna Rao
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CHAPTER 29. RIGID PAVEMENT DESIGN 29.1.4 NPTEL May 7, 2007 Equivalent radius of resisting section When the interior point is loaded, only a small area of the pavement is resisting the bending moment of the plate. Westergaard’s gives a relation for equivalent radius of the resisting section in cm in the equation 29.2. ( √ 1.6a2 + h2 − 0.675 h if a < 1.724 h b= (29.2) a otherwise where a is the radius of the wheel load distribution in cm and h is the slab thickness in cm. 29.2 Wheel load stresses - Westergaard’s stress equation The cement concrete slab is assumed to be homogeneous and to have uniform elastic properties with vertical sub-grade reaction being proportional to the deflection. Westergaard developed relationships for the stress at interior, edge and corner regions, denoted as σi , σe , σc in kg/cm2 respectively and given by the equation 29.329.5. l 0.316 P 4 log10 + 1.069 (29.3) σi = h2 b l 0.572 P + 0.359 (29.4) 4 log σe = 10 h2 b √ !0.6 3P a 2 σc = 2 1 − (29.5) h l where h is the slab thickness in cm, P is the wheel load in kg, a is the radius of the wheel load distribution in cm, l the radius of the relative stiffness in cm and b is the radius of the resisting section in cm σe Tension at Bottom σc Tension at Top σi Tension at Bottom Figure 29:1: Critical stress locations 29.3 Temperature stresses Temperature stresses are developed in cement concrete pavement due to variation in slab temperature. This is caused by (i) daily variation resulting in a temperature gradient across the thickness of the slab and (ii) seasonal variation resulting in overall change in the slab temperature. The former results in warping stresses and the later in frictional stresses. Introduction to Transportation Engineering 29.2 Tom V. Mathew and K V Krishna Rao
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CHAPTER 29. RIGID PAVEMENT DESIGN 29.3.1 NPTEL May 7, 2007 Warping stress The warping stress at the interior, edge and corner regions, denoted as σti , σte , σtc in kg/cm2 respectively and given by the equation 29.7-29.8. Et Cx + µCy (29.6) σti = 2 1 − µ2 Cx Et Cy Et σte = Max , (29.7) 2 2 r a Et σtc = (29.8) 3(1 − µ) l where E is the modulus of elasticity of concrete in kg/cm2 (3×105 ), is the thermal coefficient of concrete per o C (1×10−7) t is the temperature difference between the top and bottom of the slab, Cx and Cy are the coefficient based on Lx /l in the desired direction and Ly /l right angle to the desired direction, µ is the Poisson’s ration (0.15), a is the radius of the contact area and l is the radius of the relative stiffness. 29.3.2 Frictional stresses The frictional stress σf in kg/cm2 is given by the equation σf = W Lf 2 × 104 (29.9) where W is the unit weight of concrete in kg/cm2 (2400), f is the coefficient of sub grade friction (1.5) and L is the length of the slab in meters. 29.4 Combination of stresses The cumulative effect of the different stress give rise to the following thee critical cases • Summer, mid-day: The critical stress is for edge region given by σcritical = σe + σte − σf • Winter, mid-day: The critical combination of stress is for the edge region given by σ critical = σe + σte + σf • Mid-nights: The critical combination of stress is for the corner region given by σ critical = σc + σtc 29.5 Design of joints 29.5.1 Expansion joints The purpose of the expansion joint is to allow the expansion of the pavement due to rise in temperature with respect to construction temperature. The design consideration are: • Provided along the longitudinal direction, • design involves finding the joint spacing for a given expansion joint thickness (say 2.5 cm specified by IRC) subjected to some maximum spacing (say 140 as per IRC) Introduction to Transportation Engineering 29.3 Tom V. Mathew and K V Krishna Rao
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CHAPTER 29. RIGID PAVEMENT DESIGN NPTEL May 7, 2007 Filler h/2 Full bond No bond Figure 29:2: Expansion joint 29.5.2 Contraction joints The purpose of the contraction joint is to allow the contraction of the slab due to fall in slab temperature below the construction temperature. The design considerations are: • The movement is restricted by the sub-grade friction • Design involves the length of the slab given by: Lc = 2 × 104 Sc W.f (29.10) where, Sc is the allowable stress in tension in cement concrete and is taken as 0.8 kg/cm 2 , W is the unit weight of the concrete which can be taken as 2400 kg/cm3 and f is the coefficient of sub-grade friction which can be taken as 1.5. • Steel reinforcements can be use, however with a maximum spacing of 4.5 m as per IRC. Filler h/2 Full bond Full bond Figure 29:3: Contraction joint 29.5.3 Dowel bars The purpose of the dowel bar is to effectively transfer the load between two concrete slabs and to keep the two slabs in same height. The dowel bars are provided in the direction of the traffic (longitudinal). The design considerations are: Introduction to Transportation Engineering 29.4 Tom V. Mathew and K V Krishna Rao
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