A doubly drained soil specimen is $3cm$ thick. It is loaded from ${}_v^{\text{'}}=150$kPa to $300$kPa, leading to a change in void ratio from $1\mathrm{.}3$ to $1\mathrm{.}18.$ Its original void ratio at the start of the test is $1\mathrm{.}42.$

a$.$ If the time required for $50\%$ consolidation is $20$min., what is the coefficient of consolidation of the soil in $c\frac{m^2}{sec}?$

b$.$ How much vertical strain occurs during the loading from $150$kPa to $300$kPa $?$

c$.$ What is the permeability $($hydraulic conductivity$)$ of the soil in $c\frac{m}{sec}?$

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