As a Geotechnical Engineer at a road construction project, the student must develop the preliminary embankment geotechnical design as shown in the image below, considering the different conditioning factors, verification tests and requirements that he$/$she considered to be associated to a geotechnical work of this nature. As can be seen in the image below, the natural terrain height is of $+1,5,$ while that of the Embankment $,$ where the road platform will be built on$,$ is of $+9,5.$ The embankment$$s surface width is of $10$ meters, and it is the engineer$$s responsibility to determine the embankment$$s slope angles with the horizontal line, as well as its base width according to his$/$her engineering and design criteria. As it can be observed, the phreatic level is $1$ meter below ground surface level. The road construction project manager has explained the engineer $($the student$)$ that, as one of the embankment$$s design conditioning factors, the maximum remnant the embankment can bear is $5$ cm once the road pavement has been laid.

The terrain parameters are:

Sand:

E$=20,00$ MPa ;

u $=0,2$ ; c$=0$ kPa ; $\backslash$phi $=30$ ; $\backslash$gamma sat $=21$ kN$/$m$3$ ; $\backslash$gamma d $=19$ kN$/$m$3$

Clay:

E$=10,00$ MPa ;

u $=0,2$ ; c$=15$ kPa ; $\backslash$phi $=23$ ; $\backslash$gamma sat $=20$ kN$/$m$3$ ; $\backslash$gamma d $=16$ kN$/$m$3$ ;

The laboratory tests on the sample extracted from the middle clay stratum have provided the following results:

G $=2,7$ ; e$0=0,7$ ; Cc $=0,40$ ; Cs $=0,060$ ; cu $=$ su $=50$ kPa ; k $=2$ x $10--9$ m$/$s

Pre$-$consolidation pressure $\backslash$sigma $$p $=138$ kN$/$m$2$

Rock: The rock is massive and shows adequate conditions; width values are unknown.

RMR $=80$ ; E $=3500$ MPa ;

u $=0,2$ ; c$=1,00$ MPa ; $\backslash$phi $=45$ ; $\backslash$gamma $=24$ kN$/$m$3$

Embankment parameters:

E $=150$ MPa ;

u $=0,2$ ; c$=50,00$ KPa ; $\backslash$phi $=34$ ; $\backslash$gamma $=22$ kN$/$m$3$