Problem statement

A shallow strip foundation, $3m$ width, is embedded at $3m$ depth, just below a landfill stratum and rest on a medium strength clay of $8m$ height. In the site, the groundwater level has been measured at $4m$ depth from the ground surface. The footing is $1\mathrm{.}5m$ height and made of reinforced concrete $({}_c=25k\frac{N}{m^3})$ and is loaded by an axial vertical load, with a permanent component of $225k\frac{N}{m}$ and a variable one of $75k\frac{N}{m}.$

The physical and mechanical properties of the clay layer were measured in laboratory and by interpretation of some in situ tests. The mechanical properties were measured as linearly increasing with depth. In Table $1,$ they are reported the measured value at the top of the layer and the relative gradients.

The table also reports the main properties of the landfill soil $(3m$ height$)$ and of a sand layer that extends below the clay layer and up to a bedrock observed at $20m$ depth from the ground surface.

Table $1.$ Soil physical and mechanical properties.

$\backslash$table$[[$Unit$,$Landfill,Clay,Sand$],[$Unit weight, $[k\frac{N}{m^3}],18,20,18\mathrm{.}5],[$Initial void ratio, $e_0[-],0\mathrm{.}6,0\mathrm{.}95,0\mathrm{.}45],[$Undrained Young Modulus, $E_u[MPa],6,8,-],[$Gradient Undrained Young Modulus, $k(E_u)[MP\frac{a}{m}],-,1\mathrm{.}5,-],[$Oedometric modulus, M $[$MPa$],8,10,-],[$Gradient Oedometric modulus, $k(M)[MP\frac{a}{m}],-,1\mathrm{.}8,-],[$Poisson ratio, $v^{\text{'}}[-],0\mathrm{.}35,0\mathrm{.}35,0\mathrm{.}3],[$Pore pressure coefficients, A $[-],-,0\mathrm{.}3,-],[$Undrained shear strength, $s{u}_u[kPa],-,25,-],[$Gradient Undrained shear strength, $k(s_u)[kP\frac{a}{m}],-,10,-],[$Cohesion$,c^{\text{'}}[kPa],-,5,-],[$Friction angle, degrees$],-,20,35],[$Soil Permeability coefficient, $k[\frac{m}{s}],{10}^{-9},-,],[$Porewater coefficient, A $[-],-,0\mathrm{.}4,-]]$

It is asked to verify the foundation system to both the SLS and the ULS considering DA$2.$

The analysis has to be carried out by comparing 'traditional' analytical solutions with the numerical solutions obtained with the use of the $2$D FEA commercial code Plaxis.