Question $3$

$[12]$

A rectangular foundation for a column is to be constructed on a soil deposit as shown in the figure below. The soil is dry above the water table and fully saturated below it$.$

The soil properties are: $c^{\text{'}}=5$kPa,${}^{\text{'}}=32,=18k\frac{N}{m^3},{}_{\text{s}\text{a}\text{t}}=19\mathrm{.}5k\frac{N}{m^3}.$ Where $$ is the dry unit weight of the soil.

The load $Q$ is inclined by $=10$ to the vertical.

The depth of foundation is $D_f=0\mathrm{.}8m$ and the depth to the water table is $d=0\mathrm{.}5m.$ The dimensions of the foundation are $BL=1\mathrm{.}4m1\mathrm{.}8m,$ where the dimension $L$ is perpendicular to the plane of the figure.

Assume drained conditions and use the general bearing capacity equation to determine:

A$.$ The bearing capacity factors $N_c,N_q,$ and $N_{}.$

$[2]$

B$.$ The shape factors $F_{cs},F_{qs},$ and $F_{ys}.[2]$

C$.$ The depth factors $F_{cd},F_{qd},$ and $F_d.[2]$

D$.$ The load inclination factors $F_{cc},F_{qi},$ and $F_i.[2]$

E$.$ The ultimate bearing capacity $q_u$ of the foundation $($units of stress$).$

$3$

F$.$ The ultimate bearing load $Q$ of the foundation $($units of force$).[1]$