GET$260$s Geotechnical Engineering D$3$CIVL

Final Test $(2020\_02)$

Question $3(8$ marks$)$

An embankment in homogenous saturated clayey soil is displayed in the sketch below.

The cohesive soil has an undrained shear strength of $40k\frac{N}{m^2}$ and a bulk density of $18\mathrm{.}5k\frac{N}{m^3}.$ Calculate the factor of safety against shear slip along the surface $AB$ :

$($a$)$ Ignoring the possibility of tension cracks $(2)$

$($b$)$ Allowing for a dry tension crack $(2)$

$F_s=\frac{C_u{R}^2\frac{}{180}}{Wd}$

$($c$)$ Allowing for a tension crack filled with water $(2)$

$($d$)$ What would be the minimum factor of safety using Taylors' Stability Number if the firm stratum was deep below ground? $(2)$

Note: The area of the full segment of the slip circle is $77\mathrm{.}35m^2$ and the segment by which the slip mass area is reduced due to the tension crack can be assumed to be triangular in shape. In this case, it works out to be $5\mathrm{.}71m^2.$ The full segment internal angle, $=84$ and the reduced angle due to the tension crack, ${}_c=67\mathrm{.}4.$ The lever arm, $d,=6\mathrm{.}5m$ but reduces to $5\mathrm{.}86$ m after the tension crack appears.