Problem $2(14$ points$)$:

The sides of an excavation $2\mathrm{.}5m$ deep in the sand are to be supported by a cantilever sheet pile

frictionless wall, the water table being $1\mathrm{.}0m$ below the bottom of the excavation. The unit

weight of the sand above the water table is $17k\frac{N}{m^3}$ and below the water table the saturated

unit weight is $20k\frac{N}{m^3}.$ Characteristic parameters are $c^{\text{'}}=0,{}^{\text{'}}=35.$ Allowing for a

surcharge pressure of $10k\frac{N}{m^3}$ on the surface.

A$)$ Determine the required depth of embedment of the piling to ensure a factor of safety of $2\mathrm{.}0$

with respect to passive resistance.

Hints: you only need to consider the force balance between active thrust and passive

resistance.

B$)$ Check that the rotational and translational limit states would be satisfied for the above

embedment depth, using appropriate partial factors. We assume the design value of ${}^{\text{'}}$ takes

the conservative value by $tan\frac{{}^{\text{'}}}{1\mathrm{.}25}$ according to the limit state approach.

Hints: $1)$ you may need to update the friction angle as a designed one, that is

$1\mathrm{.}25$; $2)$ you need to consider the active thrust due to the surcharge that is multiplied by a

partial factor, we assign the number as $1\mathrm{.}3xx,$ and XX is substituted by the last two numbers of

your student ID$.$ For example, your student ID is $400522045,$ which means your partial factor is

$1\mathrm{.}345.$