Problem $1$

Concrete is required for a pavement that will be exposed to moisture and deicing salts in a severe freeze$-$thaw environment. A compressive strength of $38$ MPa at $28$ days is specified. Statistical field data available where the standard deviation is $3$ MPa.

The materials available are as follows:

$-$

Cement: Type GU$,$ meeting CSA Standard A$3001,$ with a relative density of $3\mathrm{.}14.$

$-$

Coarse aggregate: Well$-$graded, $20-$mm nominal maximum$-$size rounded gravel $($CSA A$23\mathrm{.}1)$ with an oven dry relative density of $2\mathrm{.}72,$ absorption of $1\mathrm{.}05\%$ and oven dry rodded bulk density of $1650$ kg$/$m$3.$ The laboratory sample for trial batching has a moisture content of $2\mathrm{.}2\%.$

$-$

Fine aggregate: Natural sand $($CSA A$23\mathrm{.}1)$ with an oven dry relative density of $2\mathrm{.}62$ and absorption of $0\mathrm{.}95\%.$ The laboratory sample moisture content is $5\mathrm{.}5\%.$ The fineness modulus is $2\mathrm{.}9.$

$-$

Air$-$entraining admixture: the manufacturer recommends a dosage of $0\mathrm{.}75$ g per $1$ kg of cement for $8\%$ air content.

$-$

Water reducer: This particular admixture is known to reduce water demand by $10\%$ when used at a dosage rate of $4$ g $($or $4$ mL$)$ per kg of cement. Assume that the chemical admixtures have a density close to that of water, meaning that $1$ mL of admixture has a mass of $1$ g$.$

$-$

From this information, the task is to proportion a trial mixture in the lab that will meet the above conditions and specifications.

a$)$ Write down the mix proportion while using dry aggregate as per the required strength?

b$)$ Write down the mix proportion while using SSD aggregate as per the required strength?

c$)$ Write down the mix proportion while using aggregate from stock pile as per the required strength?

d$)$ What will happen when you do not adjust the water content while using dry aggregate? What will be the expected strength?