Problem $3.[15$ points$]$

A rural principal arterial is expected to carry an ESAL of $0\mathrm{.}188{10}^6$ during the first year of operation with an expected annual growth of $6\%$ over the $20-$year design life. If the subgrade has resilient modulus of $15,000$ psi, design a suitable pavement consisting of granular subbase with layer coefficient of $0\mathrm{.}13,$ granular base layer with layer coefficient of $0\mathrm{.}14,$ and an asphalt concrete surface with layer coefficient of $0\mathrm{.}4.$ Assume all $m_i$ values $=1$ and the percent of traffic on the design lane is $47\%.$ Use reliability level of $99\%,$ standard deviation of $0\mathrm{.}4,$ and $\frac{?}{{?}_{\frac{?}{?}}}$ PSI of $2\mathrm{.}0.$ If the minimum required thickness of asphalt surface and aggregate base course is used, what is the design thickness of subbase?

Table $19\mathrm{.}9$ AASHTO$-$Recommended Minimum Thicknesses of Highway Layers

$\backslash$table$[[$Traffic$,$ ESALs,Minimum Thickness $($in$.)],[$Aspliall Concrele,Aggregare Base$],[$Less than $50\mathrm{.}000,$L$\mathrm{.}0($or surface treatment$),4],[50,001-150,000,2\mathrm{.}0,4],[150,001-500,000,2\mathrm{.}5,4],[500,001-2,000,000,3\mathrm{.}0,6],[2,000,001-7\mathrm{.}000,0100,3\mathrm{.}5,6],[$Greater than $7,000,000,4\mathrm{.}0,6]]$

Table $19\mathrm{.}4$ Growth Factors

$\backslash$table$[[\backslash$table$[[$Design$],[$Period$,],[$Years $(n)]],$Annual Growth Rate, Percent $(r)],[\backslash$table$[[$No$],[$Growth$]],2,4,5,6,7,8,10],[18,18\mathrm{.}0,21\mathrm{.}41,25\mathrm{.}65,28\mathrm{.}13,30\mathrm{.}91,34\mathrm{.}00,37\mathrm{.}45,45\mathrm{.}60],[19,19\mathrm{.}0,22\mathrm{.}84,27\mathrm{.}67,30\mathrm{.}54,33\mathrm{.}76,37\mathrm{.}38,41\mathrm{.}45,51\mathrm{.}16],[20,20\mathrm{.}0,24\mathrm{.}30,29\mathrm{.}78,33\mathrm{.}06,36\mathrm{.}79,41\mathrm{.}00,45\mathrm{.}76,57\mathrm{.}28]]$