The sieve analysis results for two aggregate piles are given below.

a$)$ In what proportions should these two piles be mixed so that the new mixture complies with the ideal gradation limits given in TS$706?($Important note: the maximum aggregate size, dmax, for the new mixture will be $16$ mm$)$

b$)$ Sketch the granulometry curve for the new aggregate pile approximately to scale.

c$)$ Calculate the fineness moduli for each mixture and the new mixture.

$-$Sieve $($mm$)$: $31\mathrm{.}5$

Retained Sample $1($g$)$: $0$

Retained Sample $2($g$)$: $415$

TS$706-$A $(\%)$: $100$

TS$706-$B $(\%)$: $100$

$-$Sieve $($mm$)$: $16$

Retained Sample $1($g$)$: $693$

Retained Sample $2($g$)$: $440$

TS$706-$A $(\%)$: $82$ TS$706-$B $(\%)$: $98$

$-$Sieve $($mm$)$: $8$

Retained Sample $1($g$)$: $655$

Retained Sample $2($g$)$: $413$

TS$706-$A $(\%)$: $70$

TS$706-$B $(\%)$: $85$

$-$Sieve $($mm$)$: $4$

Retained Sample $1($g$)$: $580$

Retained Sample $2($g$)$: $675$

TS$706-$A $(\%)$: $58$

TS$706-$B $(\%)$: $72$

$-$Sieve $($mm$)$: $2$

Retained Sample $1($g$)$: $442$

Retained Sample $2($g$)$: $800$

TS$706-$A $(\%)$: $50$

TS$706-$B $(\%)$: $68$

$-$Sieve $($mm$)$: $1$

Retained Sample $1($g$)$: $275$

Retained Sample $2($g$)$: $530$

TS$706-$A $(\%)$: $36$

TS$706-$B $(\%)$: $44$

$-$Sieve $($mm$)$: $0\mathrm{.}5$

Retained Sample $1($g$)$: $550$

Retained Sample $2($g$)$: $817$

TS$706-$A $(\%)$: $20$

TS$706-$B $(\%)$: $38$

$-$Sieve $($mm$)$: $0\mathrm{.}25$

Retained Sample $1($g$)$: $265$

Retained Sample $2($g$)$: $155$

TS$706-$A $(\%)$: $7$

TS$706-$B $(\%)$: $17$

$-$Sieve $($mm$)$: Pan

Retained Sample $1($g$)$: $480$

Retained Sample $2($g$)$: $258$

TS$706-$A $(\%)$: $0$

TS$706-$B $(\%)$: $0$