Question $1$

$1\mathrm{.}1$ In a tabular form, give the critical comparison of Rankine's and Coulomb's theories of earth pressure theorems.

$1\mathrm{.}2$ In a tabular form, give assumptions of Rankine's and Coulomb's theories of earth pressure theorems.

$1\mathrm{.}3$ The details of a gravity retaining wall are shown in the Fig. $1$ below. The unit weight of the wall concrete material $({}_{\text{c}\text{o}\text{n}\text{c}\text{r}\text{e}\text{t}\text{e}})$ is $24k\frac{N}{m^3}.$ Design for factors of safety against sliding, overturning, and tension. If the following properties is for the backfill and foundation soil respectively.

$(40)$

Backfill soil: $H=5m,i=0$;$\frac{O}{?}={40}^0$;$=(\frac{2}{3})\frac{O}{\text{;}}=18k\frac{N}{m^3}$

Foundation soil: $c=25k\frac{N}{m^2}$;$\frac{O}{?}={20}^0$;$=0\mathrm{.}75\frac{O}{\text{;}}=18k\frac{N}{m^3}$;$e=0\mathrm{.}3$

Fig$\mathrm{.}1$: Gravity retaining wall section.

$2\mathrm{.}1$ Give three $(3)$ different type of settlement and conditions by which they occur.

$(5)$

$2\mathrm{.}2$ Determine the elastic settlement of the foundation shown in Fig. $2$

$(35)$

Fig$\mathrm{.}2$: Square footing foundation.

$2\mathrm{.}1$ Give three $(3)$ different type of settlement and conditions by which they occur.

$(5)$

$2\mathrm{.}2$ Determine the elastic settlement of the foundation shown in Fig. $2$

$(35)$

Fig$\mathrm{.}2$: Square footing foundation.

Question $3$

$3\mathrm{.}1$ A variable action has an unfavourable magnitude of $Q_k=800kN.$ Considering design approach $1-$ combination $1$ with a partial factor of safety, ${}_Q=1\mathrm{.}5,$ determine the design value of the action.

$3\mathrm{.}2$ Determine the design value of a shallow foundation if the characteristics angle of shearing resistance is $\frac{O}{{?}_k^{\text{'}}}={38\mathrm{.}5}^0$ with a corresponding partial of safety of ${}_{}^{\text{'}}=1\mathrm{.}25.$

$3\mathrm{.}3$ A concrete foundation is to be cast into a soil deposit; The foundation has representative permanent actions of $G_k=1000kN,$ and $Q_k=700kN.$ If the self$-$weight, $w$ of the foundation is $50$ kN $.$ Determine the design action values using DA $-1$: C$-2.$

$3\mathrm{.}4$ A rectangular pad footing with design bearing pressure $q{E}_{Ed}$ of $690$ kPa $,$ if the design resistance value is $q_{Rd}$ of $1050$ kPa determine the percentage at which the foundation will utilize its efficiency.

$3\mathrm{.}5$ A $2\mathrm{.}52\mathrm{.}5m$ squared footing with characteristic self$-$weight $W_{Gk}=47kN$ is founded on dry sand. If the permanent and variable actions $G_k=1500kN$ and $Q_k=800kN$ are acting at the center of the foundation. Considering DA $-2,$ calculate the design bearing pressure $q_{Ed}.(3)$

$[$Marks: $15]$