Problem $5$

a$.$ Draw the flow net for the dam shown below $($datum is at the bedrock$-$soil interface$).$ The dam has two $\backslash (10-\backslash$mathrm$\{$m$\}\backslash )$ sheet piles driven partially into the granular soil layer. Redraw the schematic to scale. Use solid lines to indicate flow lines and dashed lines to indicate equipotential lines.

b$.$ Calculate the rate of seepage at the exit of the dam in $\backslash (\backslash$mathrm$\{$m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash )$ per unit length into the plane of the page. The hydraulic conductivity of the soil is $\backslash (20\backslash$times $10^\{-4\}\backslash$mathrm$\{$~cm$\}/\backslash$mathrm$\{$s$\}\backslash ).$

c$.$ Suppose that the critical hydraulic gradient for this soil is $0\mathrm{.}98.$ Do you expect piping to occur at the dam exit?