To calculate the surface deflection under the center of a tire, we can use the two-layer theory which considers the pavement layer and the subgrade layer. The formula for the surface deflection is given by:
δ = (P/a) * (1-v) * (h1/((E1/((1-v1^2) + (E2/((1-v2^2))))))
Where,
P = tire pressure = 552 kPa
a = contact area of the tire = 152 mm
v = Poisson's ratio
h1 = thickness of the pavement layer = 305 mm
E1 = modulus of elasticity of the pavement layer = 345 MPa
v1 = Poisson's ratio of the pavement layer
E2 = modulus of elasticity of the subgrade layer = 69 MPa
v2 = Poisson's ratio of the subgrade layer
Substituting the given values in the above formula, we get:
δ = (552/152) * (1-0.25) * (305/((345/((1-0.25^2) + (69/((1-0.3^2))))))
δ = 3.029 mm
The interface deflection can be calculated as:
δi = (P/a) * ((h2 * (E1/((1-v1^2) + (E2/((1-v2^2))))))
Where,
h2 = thickness of the subgrade layer
Substituting the given values in the above formula, we get:
δi = (552/152) * ((0.0 * (345/((1-0.25^2) + (69/((1-0.3^2))))))
δi = 0 mm
As there is no thickness of subgrade layer given, the interface deflection is zero.
The deflection that takes place within the pavement layer can be calculated as the difference between the surface deflection and the interface deflection:
δp = δ - δi
δp = 3.029 - 0
δp = 3.029 mm
Therefore, the surface deflection under the center of a tire is 3.029 mm, the interface deflection is 0 mm, and the deflection that takes place within the pavement layer is 3.029 mm.
