Problem $10\mathrm{.}11$

$($a$)$ What is the limit bearing capacity $($qbL$)$ of a strip footing with width B $=1$ m on the surface of a sand deposit with DR $=70\%?$ The sand has a unit weight equal to $19$ kN$/$m$3$ and a critical$-$state friction angle $$c of $31.$ Assume the water table to be deep.

$($b$)$ What is the limit bearing capacity for relative density of $90\%?$

$($c$)$ What is the limit bearing capacity ignoring the contribution of dilatancy?

Problem $10\mathrm{.}12$

Consider that the footing of Problem $10\mathrm{.}11$a is embedded $0\mathrm{.}6$ m in the ground, that is$,$ D $=0\mathrm{.}6$ m$.$ What is the limit resistance of the footing now?

Problem $10\mathrm{.}13$

Consider a $1$ m square instead of a strip footing on the surface of the soil deposit of Problem $10\mathrm{.}11$a$.$ What is the limit resistance of the footing? Problem

$10\mathrm{.}14$

Consider that the footing of Problem $1013$ is embedded $0\mathrm{.}6$ m in the ground, that is$,$ D $=0\mathrm{.}6$ m$.$ What is the limit resistance of the footing now?

Problem $10\mathrm{.}16$

Redo Example $10\mathrm{.}13$ considering the water table to be located at a depth at the ground surface. Consider the saturated unit weight of the soil to be equal to $22$ kN$/$m$3.$