Concrete Mixture design Additional Example

Concrete is required for a slab on grade that will be exposed to moisture in a severe freezethaw environment. A specified compressive strength, $Fc$ of $35$MPa is required at $28$ days. Air entrainment is required. Slump should be between $25mm$ and $75mm.$ No statistical data on previous mixes are available. The materials available are as follows:

Cement: Type GU $($ASTM C $1157)$ with a relative density of $3\mathrm{.}0.$

Coarse aggregate: 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 $2\%.$

Fine aggregate: Natural sand $($ASTM C $33$ or AASHTO M $6)$ with an oven dry relative density of $2\mathrm{.}64$ and absorption of $0\mathrm{.}7\%.$ The laboratory sample moisture content is $6\%.$ The fineness modulus is $2\mathrm{.}80.$

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

Water reducer: ASTM C $494($AASHTO M $194).$ This particular admixture is known to reduce water demand by $10\%$ when used at a 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 $1g.$

Determine the estimated sand weight for batch of one cubic meter of concrete.