Problem $2$: Resilient modulus of fine$-$grained material

Consider table $1$ below, which give the test results to measure the Resilient Modulus, Mr$,$ for a granular material.

a$)$ Calculate $M_t$ for each of the test conditions provided.

b$)$ Plot $M_r$ vs$.{}_4$ and determine the coefficients $k_1,k_2,k{k}_3$ and $k{a}_4.$

c$)$ Estimate $M_r$ for design given the asphalt institute recommendations for ${}_3$ and ${}_d.$

Table $1$ Resilient modulus test results

$\backslash$table$[[$Sequence No$,\backslash$table$[[$Deviator$],[{}_d($psi$)]],\backslash$table$[[$Confining$],[{}_3($psi$)]],$Recovered strain $e_r($x ${10}^{-3})],[1,1,6,0\mathrm{.}098],[2,1,3,0\mathrm{.}104],[3,1,0,0\mathrm{.}114],[4,2,6,0\mathrm{.}204],[5,2,3,0\mathrm{.}271],[6,2,0,0\mathrm{.}260],[7,4,6,0\mathrm{.}513],[8,4,3,0\mathrm{.}556],[9,4,0,0\mathrm{.}755],[10,8,6,1\mathrm{.}428],[11,8,3,1\mathrm{.}778],[12,8,0,2\mathrm{.}353],[13,10,6,1\mathrm{.}923],[14,10,3,2\mathrm{.}778],[15,10,0,4\mathrm{.}00]]$