Problem No$.2$: $15$ Points

Consider the sheet pile driven in soil with a permeability coefficient of $9\mathrm{.}3{10}^{-5}\frac{m}{sec}$ as shown in Figure $2.$ The saturated unit weight of the soil is $17K\frac{N}{m}3.$

a$.$ Calculate the flow rate per $1m$ in the longitudinal direction. $(5$ points$)$

b$.$ Check the stability of the brown area $(10m5m)$ against heave points$)$

Figure $2$

SAFETY AGAINST BOILING

$F.S.=\frac{i_c}{i_e}$

F$.$S$.$: Factor of Safety

$i_c$ : critical hydraulic gradient

I: exit hydraulic gradient

CRITICAL HYDRAULIC GRADIENT $)i_c=\frac{{}^{\text{'}}}{{}_w}=\frac{G_s-1}{v},i_c=\frac{{}^{\text{'}}}{{}_w}=\frac{G_s-}{1+e}$

EXIT HYDRAULIC GRADIENT $(($:$i_d\}$

$i_e=\frac{h}{L}=\frac{\frac{H}{N}d}{l}$

APPLICATION OF THE FLOW NET

We can use the Flow$-$Net, the number of the head drops $($Nd$)$ and flow channels $(Nf),$ to estimate the followings: $-$

$1-$ Pressure head $(h_p)$ from head of water $(h)$ in upstream at different points in the net then determining the pore water pressure $(u),$ where: $-$

$u={}_w^{**}{h}_p$

$2-$ Quantity of seepage through the flow path,

$Q=k*H\frac{NN}{Nd}*L$

$3-$ Safety against boiling and Exit gradient $(($:$i_e\},$ where: $-$

$F.S.=\frac{i_c}{i_e}$

Where: $I=$ length of last square side at exit of water