Question $1)$ A breakwater to be designed in $9m$ water depth, where the bottom slope is $\frac{1}{40},$ deep water significant wave height is $H_{50}=4\mathrm{.}5m,$ and period is $T=9s.$ Waves are approaching to the shore in the setup when bathymetric lines make $10$ degrees to the crestlines. Stone of $10$ tonnes of maximum mass can be obtained from the local quarry. Determine the appropriate breakwater slopes, layer thicknesses, crest widths and crest elevations for the head and trunk sections of the structure. Draw the head and trunk sections of the rubblemound breakwater you have dimensioned. $({}_t=2\mathrm{.}6\frac{t}{m^3},{}_s=1\mathrm{.}02\frac{t}{m^3}).$

$W=\frac{{}_t{H}^3}{K_D(\frac{{}_t}{{}_s}-1{)}^{3}cot},\frac{R_u}{H_0}=1\mathrm{.}016tan(\frac{H_0}{L_0}{)}^{-0\mathrm{.}5}r,t=n{K}_D^{\text{'}}(\frac{W}{{}_s}{)}^{\frac{1}{3}}$

Table. $K_D,K_D$ ve $r$ values $($CERC$,1984)$

$\backslash$table$[[$Protective layer,$\backslash$table$[[$Armor$],[$unit $($n$)]],$K$\_($D$)^(\text{'}),$r$,$K$\_($D$),$ stability coefficient,$\backslash$table$[[$Slope$],[($cot$\backslash$alpha $)]]],[$Structure trunk,Structure head$],[\backslash$table$[[$Breaking$],[$waves$]],\backslash$table$[[$Non$-$breaking$],[$waves$]],\backslash$table$[[$Breaking$],[$waves$]],\backslash$table$[[$Non$-$breaking$],[$waves$]]],[\backslash$table$[[$Rough$,$ angular$],[$quarrystone$]],2,1\mathrm{.}00,0\mathrm{.}37,2\mathrm{.}0,4\mathrm{.}0,1\mathrm{.}9,3\mathrm{.}2,1\mathrm{.}5],[1\mathrm{.}6,2\mathrm{.}8,2\mathrm{.}0],[1\mathrm{.}3,2\mathrm{.}3,3\mathrm{.}0],[\backslash$table$[[$Rough$,$ angular$],[$quarrystone$]],>3,1\mathrm{.}00,0\mathrm{.}40,2\mathrm{.}2,4\mathrm{.}5,2\mathrm{.}1,4\mathrm{.}2,1\mathrm{.}5-3\mathrm{.}0],[$Tetrapod$,2,1\mathrm{.}10,0\mathrm{.}50,7\mathrm{.}0,8\mathrm{.}0,5,6\mathrm{.}0,1\mathrm{.}5],[4\mathrm{.}5,5\mathrm{.}5,2\mathrm{.}0],[3\mathrm{.}5,4\mathrm{.}0,3\mathrm{.}0]]$