Question $1$

A rectangular concrete foundation is to support a load bearing wall and is to be

founded at a depth of $1\mathrm{.}5m$ in a deep deposit of dense sand. The dimensions of the

foundation are:

length $=6\mathrm{.}0m$

width $=2\mathrm{.}0m$

thickness $=0\mathrm{.}8m$

The angle of shearing resistance of the sand is $32$ and its unit weight is $20k\frac{N}{m^3}.$

The unit weight of concrete is $24k\frac{N}{m^3}.$

The load bearing wall will act on the centre$-$line of the foundation as shown in Figure

Q$1.$ Also acting is a permanent horizontal force as shown. The magnitudes of the

forces are:

Permanent Vertical load, $V=200k\frac{N}{m}$ run

Permanent Horizontal load, $H=50k\frac{N}{m}$ run

No temporary $($variable$)$ actions act on the foundation.

Establish the magnitude of the over$-$design factor for the Eurocode $7$ bearing

resistance $($GEO$)$ limit state, using Design Approach $2.$

Figure Q$1$: Diagram of foundation $($from two views$).$

Note: The combined vertical and horizontal loading will of course create an inclined

resultant force. To aid your calculations, the following inclination factors are provided

for you. All other factors should be determined using the tables and formulae provided

at the end of the paper.

$i_c=0\mathrm{.}69$

$i_q=0\mathrm{.}70$

$i_{}=0\mathrm{.}57$