Question No$.5[15$ Marks$]$

You were hired to design a concrete mixture to cast a multi$-$storey car parking with a minimum slab thickness of $150mm$ and a minimum width for columns of $400mm$ for all levels. Based on the selected location, the concrete elements will be exposed to moisture in a severe freeze$-$thaw environment. A specified compressive strength of $36$MPa is required at $28$ days. Air entrainment is required. The slump should be $50mm.$ No statistical data on previous mixes are available. The local materials supplier sent you the list of the available materials in the stoke. For the fine aggregate, they order natural sand with a fineness modulus of $2\mathrm{.}8$ from a nearby quarry.

The materials available are as follows:

Cement: Type GUb$-$FA cement, with a relative density of $3\mathrm{.}0$ and fly ash content of $10\%.$ Coarse aggregate I: Well$-$graded, $25-mm$ nominal maximum$-$size rounded gravel $($ASTM C$33$ or AASHTO M $80)$ with an oven$-$dry relative density of $2\mathrm{.}68,$ absorption of $0\mathrm{.}5\%($moisture content at SSD condition$)$ and oven$-$dry rodded bulk density $($unit weight$)$ of $1600k\frac{g}{m^3}.$ The laboratory sample for trial batching has a moisture content of $2\%.$

Coarse aggregate II: Well$-$graded, $75-mm$ nominal maximum$-$size rounded gravel $($ASTM C$33$ or AASHTO M $80)$ with an oven$-$dry relative density of $2\mathrm{.}89,$ absorption of $0\mathrm{.}6\%($moisture content at SSD condition$)$ and oven$-$dry rodded bulk density $($unit weight$)$ of $1750k\frac{g}{m^3}.$ The laboratory sample for trial batching has a moisture content of $3\mathrm{.}2\%.$

Air$-$entraining admixture: Wood$-$resin type $($ASTM C $260$ or AASHTO M $154).$ The manufacture recommends a dosage of $0\mathrm{.}5gm$ per $kg$ of cement.

Water reducer: ASTM C $494($AASHTOM$194).$ The recommended dosage rate of $3g($or $3mL)$ per $kg$ of cement.

Assume that the chemical admixtures have a density close to that of water, meaning that $1mL$ of admixture has a mass of $1g.$ Assume a density of water of $997\mathrm{.}75k\frac{g}{m^3}.$

Determine the required volume of fine$-$aggregate to send a request for the quarry.