how solve this question A local road is required to be const

how solve this question, A local road is required to be constructed which consists of a layer of asphalt-treated stone on top of compacted subgrade. Assume that the design single wheel load is 18,000 lb and the tire pressure is 80 psi. It is required that the deflection at the surface of the stone layer not to exceed 0.2 in. What is the minimum thickness of the stone layer in order to satisfy this requirement? The moduli of elasticity of the stone layer and the subgrade material are 40,000 and 4,000 psi.

Solution

Solution:-

Given

Design single wheel load (P) =18000 lb

Tire pressure (p) = 80 psi

Deflection () = 0.2 inch

Modulus of elasticity of stone layer (E₂) = 40000 psi

Modulus of elasticity of subgrade layer (E₁) = 4000 psi

Radius of contact (a) = (P/(*p))

= (18000/(*80))

= 8.46 inch

Deflection for wheel load is given by

= 1.5*p*a *F/E₁

0.2 = 1.5 * 80*8.46 *F/4000

F = 0.78

E₁/E₂ =4000/40000 =0.1

From value of F=0.78 and E₁/E₂ =0.1   We can calculate value of h/a

h/a =0.42   (from graph)

thickness of stone layer (h) = 0.42 *8.46

= 3.55 inch    Answer