Question $3$

$($a$)$ The following notes refer to a $1200m$ section of a proposed railway and the carthwork distribution in this section is to be planned without regard to the adjoining sections. The table below shows the stations and the surface levels along the centre line, the formation level being at an clcvation above datum of $43\mathrm{.}50m$ at chainage $70$ and thence rising uniformly on a gratient of $1\mathrm{.}2\%.$ The volumes are recorded in $m^3,$ the cuts are plus and fills minus.

$\backslash$table$[[$Chn$.,\backslash$table$[[$Surface$],[$Level$]],$Vol.,Chn$.,\backslash$table$[[$Surface$],[$Level$]],$Vol.,Chn$.,\backslash$table$[[$Surface$],[$Level$]],$Vol.$],[70,52\mathrm{.}8,,74,44\mathrm{.}7,,78,49\mathrm{.}5,],[,,+1860,,,-1080,,,-237],[71,57\mathrm{.}3,,75,39\mathrm{.}7,,79,54\mathrm{.}3,],[,,+1525,,,-2025,,,+362],[72,53\mathrm{.}4,,76,37\mathrm{.}5,,80,60\mathrm{.}9,],[,,+547,,,-2110,,,+724],[73,47\mathrm{.}1,,77,41\mathrm{.}5,,81,62\mathrm{.}1,],[,,-238,,,-1120,,,+430],[74,44\mathrm{.}7,,78,49\mathrm{.}5,,82,78\mathrm{.}5,]]$

Use the table above to prepare a M$.$H$.$D$.$ and answer these questions.

$($i$)$ Assuming a correction factor of $0\mathrm{.}8$ applicable to fills, plot the M$.$H$.$D$.$ to a vertical scale of $1000m^3$ to $20mm.$

$($ii$)$ Calculate total haul in station metres and indicate the haul limits on the curve and section.

$($iii$)$ State which of the following estimates you would recommend:

No freehaul at $35ppe{r}^3$ for excavating, hauling, and filling.

A treehaul distance of $300m$ at $30$ p per $m^3$ plus $2$ p per stn$.m$ for overhaul.

$(17$ marks$)$

$($b$){}_n$ embankment was constructed with a formation width of $14\mathrm{.}00m$ and a formation level of $85\mathrm{.}43m.$ The ground slope at right angles to the centerlinc was $1$ in $8$ and the side slopes were $1$ in $2.$ Sketch and calculate the cross$-$sectional area of the roadway.

$(8$ marks$)$