The resilient modulus test data on a subgrade soil sample in table $1$ includes recoverable

deformations $(($in$/$in$)),$ confining stresses $($c $($psi$)),$ and deviatoric stresses $($d $($psi$)).$ The

distance between the LVDT clamps $($deformation measuring device$)$ is $4$ in$.$ Using this data

determine:

a$.$ Mr for each successful loading sequence of confining and deviator stresses

b$.$ Mr equation for all the combinations of confining stresses and loading levels, as a function of the

bulk stress and the deviator stress.

c$.$ Recommend the best values of constants for the right relationship of the Mr equation in $($b$)$ based

on the R$2$ value.

Table $1$: Resilient Modulus Test data on a subgrade soil

Confining

pressure

$($c$)($psi$)$

Deviator

stress

$($d$)$ psi$)$

Recoverable

deformation

$(0\mathrm{.}001$ in$)$

$2010\mathrm{.}000264$

$2020\mathrm{.}000496$

$2050\mathrm{.}001184$

$20100\mathrm{.}002284$

$20150\mathrm{.}003428$

$20200\mathrm{.}004420$

$1510\mathrm{.}000260$

$1520\mathrm{.}000512$

$1550\mathrm{.}001300$

$15100\mathrm{.}002500$

$15150\mathrm{.}003636$

$15200\mathrm{.}004572$

$1010\mathrm{.}000324$

$1020\mathrm{.}000672$

$1050\mathrm{.}001740$

$10100\mathrm{.}003636$

$10150\mathrm{.}003872$

$510\mathrm{.}000508$

$520\mathrm{.}000988$

$550\mathrm{.}002224$

$5100\mathrm{.}003884$

$5150\mathrm{.}005768$

$110\mathrm{.}000636$

$120\mathrm{.}000880$

$150\mathrm{.}002704$

$17\mathrm{.}50\mathrm{.}003260$

$1100\mathrm{.}004444$