AASHTO design: find initial commercial vehicles

Given and assumptions

Surface 5.3 in ($E_1=365$ ksi), base 8.6 in ($E_2=30$ ksi, $m_2=1$), subgrade $E_3=9$ ksi $=M_R=9000$ psi. Reliability, standard deviation and $\Delta PSI$ are not given for this part; the values of the companion problem are used: $R=90\%$ ($Z_R=-1.282$), $S_0=0.5$, $\Delta PSI=2.0$. Two-lane two-way road: design lane carries 50 percent of the total.

Step 1 - Layer coefficients and SN

$$\begin{aligned} a_1&=0.323\log_{10}(365000)-1.42=0.377\\ a_2&=0.249\log_{10}(30000)-0.977=0.138\\ SN&=a_1D_1+a_2D_2m_2=0.377\times5.3+0.138\times8.6\times1=3.18 \end{aligned}$$

Step 2 - ESALs the section can carry (AASHTO-93)

$$\log_{10}W_{18}=Z_RS_0+9.36\log_{10}(SN+1)-0.20+\frac{\log_{10}[\Delta PSI/2.7]}{0.4+1094/(SN+1)^{5.19}}+2.32\log_{10}M_R-8.07$$

Substituting $SN=3.18$, $M_R=9000$: $\log_{10}W_{18}=5.954$, so $W_{18}=900251$ ESALs.

Step 3 - Initial commercial vehicles per day

Growth factor for 10 years at 6 percent: $\dfrac{(1.06)^{10}-1}{0.06}=13.181$.

$$W_{18}=365\times A\times0.5\times VDF\times GF \ \Rightarrow\ A=\frac{900251}{365\times0.5\times2.5\times13.181}=149.7\ \text{CVPD}$$

This is the traffic in the year the road opens. The construction period is 2 years, so the traffic counted at the start is

$$A_0=\frac{149.7}{(1.06)^2}=133.2\ \text{CVPD}$$

Answer: the pavement was designed for an initial traffic of about 133 commercial vehicles per day (at the time of the survey), which grows to about 150 CVPD at opening.