A cross$-$section through a concrete gravity dam spillway and the underlying foundation soils is shown in Figure $2.$ Also shown is a flownet for the seepage of water from the reservoir through the soils below the dam and spillway. The saturated unit weight of the soils can be take as $\backslash (19\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$ Lab testing on samples of the soil at this site suggest that the permeability is around $\backslash (4\backslash$times $10^\{-6\}\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$

Figure $2$: Cross section through concrete dam spillway and associated flownet

$($a$)$ Calculate the head $($relative to the water table on the downstream side of the dam$)$ at points $\backslash (\backslash$mathrm$\{$A$\},\backslash$mathrm$\{$B$\}\backslash ),$ C$,$ D and E in Figure $2.$ State your answers in meters.

$(8$ marks$)$

$($b$)$ Calculate the water pressure at points A$,$ B$,$ C$,$ and D in Figure $2.$

$(4$ marks$)$

$($c$)$ Estimate the vertical effective stress at point D$,$ assuming that the vertical total stresses are unaffected by the presence of the dam.

$($d$)$ Calculate the rate of seepage per meter of dam length $($into the page$).$ You should give your answer in $\backslash ($ m$^\{3\}/$ d a y $/$ m $\backslash ).$

$($e$)$ If the dam is $200$ m long $($i$.$e$.$ into the page$),$ what is the total expected seepage flow.

$(1$ mark$)$

$($f$)$ Explain why geotechnical engineers might be concerned about upward seepage flow, especially near the soil surface $($i$.$e$.$ at the ground surface or in an excavation$).$

$($g$)$ Estimate the hydraulic gradient at point C in Figure $2.$

$($h$)$ Calculate the hydraulic gradient at point E $.$ Do you expect any issues due to the seepage at this location?

$($i$)$ State any assumptions which have been made in your calculations.