Question $1(50$ Marks$)$

A regional road is to be constructed along the base of the slope illustrated in Figure $1.$ It is proposed to

construct a retaining wall to ensure the stability of the residential structures on the top of slope terrain

and also to avoid any future problems to the transportain activity on the regional road.

a$)$ Model and proportion a cantilever retaining wall that can be useful in the scenario illustrated in

Figure $1($Hint: Chapter $6,$ Slide $11).$ The slope has a vertical height of $4m,$ and the depth of

the retaining wall foundation $(D_f)$ should be $1\mathrm{.}5m$ below the surface. The backfill is placed

horizontally. $(20$ marks$)$

Note:

To ensure the safety and stability of the retaining wall it is necessary to ensure the FS values for

overturning and sliding are met in part $($b$).$ Following the proportioning guidelines, model the

proposed retaining for the scenario summarized in $($a$).$ This exercise may require a couple of trials to

refine the model to achieve the requisite FS values. the design. Failure of the retaining wall due to

overturning or sliding is likely if appropriate proportioning is not acheived. Make atleast two attempts

to satisfy the design guidelines. If you are not able to achieve the objective, provide a discussion on the

necessary changes that you suggest to achieve the requiste FS requirements.

b$)$ Determine the Factor of Safety $($FS$)$ against overturning and sliding $($Neglect passive

resistance, $P_p)$ about the toe of the cantilever retaining wall modelled in part $($a$)$ using

Rankine's earth pressure theory. The unit weight of the concrete is $23\mathrm{.}5k\frac{N}{m^3}.$ Assumptions;

GWT several meters below the surface, $k_1=k_2=\frac{2}{3}.(30$ marks$)$