CT4860 STRUCTURAL DESIGN OF PAVEMENTS

stress at the bottom of the concrete slab) can be calculated using the theory
of elasticity (21):
σs =
2
π
'
h E δ m
4
2
T
2 ( 1 − υ )
α
(42)
where: σs = flexural tensile stress (N/mm 2 )
h = thickness (mm) of the concrete slab
υ = Poisson’s ratio of concrete
E’ = fictitious modulus of elasticity (N/mm 2 ) of concrete, taking into
account the stress relaxation because of the static settlement
loading (E’ ≈ Ec/3)
δm = difference (mm) of level of highest and lowest point (i.e. two times
the amplitude) of the sinusoidal settlement profile
T = halve the wave length (mm) of the sinusoidal settlement profile
α = factor, dependent on the wave length T, the slab length L and the
ratio of the modulus of substructure reaction k and the radius of
relative stiffness l:
α = 1 – F cos ⎟ ⎛π
L ⎞
⎜
(43)
⎝ 2 T ⎠
where: F = factor, dependent on the ratio of the slab length L and
the radius of relative stiffness l (figure 22)
Unequal settlements usually are greatest in the longitudinal direction of a
road.
For the normally applied concrete qualities, concrete slab thicknesses and
moduli of substructure reaction the reduction factor α is (nearly) 1 in case of a
slab length L of more than about 4 m, which is usually the case for plain
concrete pavements.
For reinforced concrete pavements (slab length = distance between the
cracks = 1.5 to 3 m) the factor α is smaller than 1. This leads to a reduction of
the settlement flexural stresses. The smaller the ratio of the modulus of
substructure reaction k and the radius of relative stiffness l of the concrete
slab and the smaller the slab length L, the smaller the factor α and thus the
smaller the settlement stresses.
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