$1.(20$ points$)$ Problem $12\mathrm{.}7$ on Textbook, page $599,$ also attached below. Note that Problem $12\mathrm{.}7$ ask you to solve the problem use both design equation and the design chart.

$2.(15$ points$)$ Problem $12\mathrm{.}8$ on Textbook, page $599,$ also attached below.

$3.(15$ points$)$ Use Caltrans design procedure to determine a JPCP concrete pavement layers thickness for a Traffic Index of $12\mathrm{.}5.$ Assume the pavement will be located in an climate zone of Central Coast area, with the soil of CL $($inorganic clays of low to medium plasticity$)$ with a R$-$value of $30.$ Assume there is not lateral support along the longitudinal joints.

$12\mathrm{.}7$ Figure P$12\mathrm{.}7$ shows a concrete pavement with the thicknesses and elastic moduli as indicated. Assume a modulus of rupture of $650$ psi, a load transfer coefficient of $3\mathrm{.}2,$ a serviceability loss from $4\mathrm{.}5$ to $2\mathrm{.}0,$ and poor drainage with $\backslash (5\backslash \%\backslash )$ of time near saturation. Determine the performance traffic by Eq$.12\mathrm{.}21$ without the reliability term and check the result by the AASHTO design chart. $[$Answer: $\backslash (8\mathrm{.}5\backslash$times $10^\{6\}\backslash )]$

GURE P$12\mathrm{.}7$

$12\mathrm{.}8$ A $\backslash (8\mathrm{.}5-\backslash$mathrm$\{$in$\}\backslash ).(\backslash (216-\backslash$mathrm$\{$mm$\}\backslash ))$ concrete slab is placed directly on a subgrade. The relationship between the resilient modulus and $\backslash ($ k $\backslash )$ value is indicated by Eq$.12\mathrm{.}22.$ The monthly subgrade resilient moduli from January to December are $15,900,27,300,38,700,50,000,900,1620,\backslash (2340,3060,3780,4500,4500\backslash ),$ and $4500$ psi $.$ Determine the effective modulus of subgrade reaction. $[$Answer: $305$ pci $]$