$(5$ pts$.)$ As a pavement designer, you are asked to check if the following structural design of asphalt pavement $($see Figure $1)$ is acceptable for preventing severe fatigue cracking under traffic for a $20-$year design period. Use Miner's Law $($see below$)$ to estimate the fatigue damage and a $3-$layer model to determine the structural responses.

Design Conditions

Traffic: one million repetitions of a standard $18-$kip dual$-$tire axle $($i$.$e$.,1,000,000$ ESALs$)$ for $20$ years

Loading configuration: single axle and single tire with a load of $4500$ lb and a tire pressure of $100$ psi

Pavement structure: three layers with asphalt surface $(2\mathrm{.}35$ in$.),$ stabilized base $(4\mathrm{.}7$ in$.),$ and subgrade $($infinite depth$)$

The material properties of each layer are also presented in Figure $1.$

Pavement Fatigue Cracking Model

Fatigue cracking $N_f=(\frac{0\mathrm{.}005889}{{}_t}{)}^5,$ where $N_f$ is the allowable number of load repetitions and ${}_t$ is the tensile strain at the bottom of the asphalt layer.

Miner's law

Fatigue cracking damage, D $D=(\frac{n_f}{N_f}),$ where $n_f$ is the actual traffic for the design period.

Figure $1$ Three$-$layer asphalt pavement under a single tire

$1$