The design of rigid pavements involves the design of the thickness of the cement concrete slab comprising the rigid pavement, since the pavement derives its structural strength primarily through the flexural strength of the slab. Except for low traffic volumes and street roads, reinforced cement concrete (RCC) slabs are used as rigid pavements.
In addition to the design of thickness, the design of reinforcements, dowel bars, tie-bars and the design of joints are also factors to be considered for ensuring successful performance of the pavement.
The stresses in the pavement due to temperature changes and consequent warping, and those due to frictional forces have also to be determined in addition to stresses due to wheel loads and their repetitions. The resultant stresses due to the combined action of these are computed and the consequent deformations or deflections in the pavement slab are ensured to be within allowable limits.
Some of the design considerations, such as traffic- related factors, subgrade strength, climate- and environment-related factors, reliability, and economic factors – all of these apply as much to rigid pavement design as they do for flexible pavement design.
In addition, factors specific to rigid pavement design are given below:
1. Provision of Sub-Base/Base:
The functions of sub-base/base course are:
(i) To provide a levelling course on a rough subgrade.
(ii) To provide a reasonably firm support to the pavement
(iii) To act as a cut-off to prevent damage due to capillary rise.
(iv) To minimise damage due to forest heave, if any.
(v) To prevent mud-pumping in fine grained soils.
The materials commonly used for sub-base/base are:
(i) Well-graded gravel-stand mixtures
(ii) Lime- or cement-stabilised soil
(iii) Lime pozzolona concrete or lean cement concrete
(iv) Water bound macadam (WBM) layers.
Sub-bas/base courses certainly add strength to the subgrade. Though weak spots, if any, in the subgrade can be bridged by a rigid pavement, it would be preferable to provide sub- base/base course for rigid pavements to serve high-volume/heavy traffic.
2. Properties of Cement Concrete:
As cement concrete is the primary component of a rigid pavement, its properties relevant to its performance under traffic are of interest.
The following are the important properties:
The design of the pavement slab is dependent upon the strength of cement concrete. The most commonly used property is the compressive or crushing strength. Concrete has a relatively high compressive strength and so it rarely fails in compression in a pavement slab. The flexural strength of concrete is the more important factor; this is determined usually by conducting a bending test on a beam of square cross-section, 150 mm x 150 mm, with a span of 700 mm.
The load is applied at the third points of the span. The modulus of rupture is the flexural strength; a minimum of 4 MN/m2 (40 kg/cm2) is specified by the IRC. (IRC: 58-2002). For this, the 28-day compressive strength of concrete should be a minimum of 30 MN/m2 (300kg/cm2).
(ii) Modulus of Elasticity and Poisson’s Ratio:
The more the strength, the more is the modulus of elasticity (Ec) of the concrete. This governs the ‘relative stiffness of the slab, given later, and so it is an important design factor. It may be found by the static method or dynamic method of testing. Ec is about 3 x 104 MN/m2 (3 x 105 kg/cm2) for concrete with a flexural strength in the range of 3.8 to 4.2 MN/m2 (38 to 42 kg/cm2)
Poisson’s ration (ϒ) also will be needed in the determination of stresses in concreted slabs. It may be determined either by static or dynamic method, the value of ϒ ranging from 0.15 to 0.24.
(iii) Shrinkage of Concrete:
During setting, concrete expands slightly, but it shrinks during subsequent drying; this phenomenon of shrinkage causes some stresses in concrete. Subsequent moisture variations may also cause shrinkage/expansion, resulting in additional stresses.
(iv) Fatigue Behaviour of Concrete:
Repetitive traffic loading causes progressive internal damage to concrete. Research into this aspect has revealed that as the ratio of the flexural stress to flexural strength (the ratio being called ‘stress ratio’) increases, the resistance of concrete to repetitive loading decreases, and it can withstand only fewer and fewer repetitions. Interestingly, it has been found that when this stress ratio does not exceed 0.55, concrete can withstand unlimited stress repetitions without any reduction in load-carrying capacity.
But “IRC: 58-2002” gives a more conservative value of 0.45 for the stress ratio for unlimited repetitions.
A few typical values of allowable repetitions for certain chosen stress ratios are given in Table 7.14 (IS: 58-2002).
3. Temperature Changes:
Changes in the temperature gradient through the pavement slab cause differential expansion or contraction between the top and bottom of the slab. As a result of this, the slab tends to warp; but, this tendency is counteracted by the weight of the slab and friction at load-transfer devices at joints. Stresses induced because of temperature changes are known as ‘warping’ or ‘temperature’ stresses.
A slab can be plain or un-reinforced or reinforced. For highways meant to serve high-volume traffic with heavy loads and load repetitions, the pavement slab has to be necessarily reinforced. The amount and distribution of reinforcements is an important design factor. Recent advances in continuously reinforced cement concrete pavement have improved the design procedures significantly.
Joints are necessary in cement concrete pavements for allowing for expansion, contraction, and warping, as well as for construction in convenient stretches or bays. The spacing and treatment of joints affect the stresses induced in the pavement slab.
The frictional force between the slab and the sub-base/subgrade soil below determines the resistance imposed on expansion and contraction due to changes in temperature – seasonal as well as daily changes. Spacing of joints also is, to some extent, governed by this friction. Thus, the stresses caused in the pavement on this score are called frictional stresses.
Compacted sand and gravel covered with waterproof paper provide a smooth surface. Usage of water-bound macadam (WBM), gravel-sand mixtures, lean concrete or lime pozzolona concrete as base/sub-base between the subgrade and the pavement provides a relatively rough surface.
Thus, the resultant stresses in the pavement are due to the combined action of wheel loads, warping due to temperature changes and the restraint due to frictional forces at the interface.
7. Special Considerations Regarding Wheel Load and Repetitions:
Wheel loads induce stresses on cement concrete slabs used as rigid pavements. Axle loads on a highway fall within a wide range. Varying axle loads are converted in terms of a single standard axle load, which is 80 kN in India. For the basic design of the slab, 98 percentile axle load is chosen; this is multiplied by a load safety factor (LSF) to take care of unexpected heavy truck loads. For important highways like the National Highways, LSF of 1.2 is used.
Impact is another important factor in the design of concrete slabs; this is minimised by the provision of effective load-transfer devices at joints; in such a case, the stresses due to static wheel loads are increased by 25% to account for impact. In the absence of such load-transfer devices, the stresses are increased by 50% and the resulting stress is checked against the allowable stresses in cement concrete.
Repetitive loading has been found to have a significant effect on the performance of a rigid pavement. As the number of repetitions increases, the serviceability index decreases because cement concrete suffers fatigue under repeated load applications. Hence, any design procedure has to account for the effect of load repetitions in the same manner. A design period of 20 years is usually considered.