Illustrative Example $19\mathrm{.}8.$ Determine the active thrust on the retaining wall shown in Fig. E$-19\mathrm{.}8.$ The backfill is cohesionless $)=30,=19k\frac{N}{m^3},=(20.$

Solution. The method of trial wedges is used $($Sect$.19\mathrm{.}12).$ Several trial planes such as $B-1,B-2,B-3,B-4$ are chosen. The sliding wedge is in equilibrium under the three forces $W,R$ and $P_{}.$ The weights of the wedges are computed as given below.

Wedge $AB1,$

Wedge $AB2,$

Wedge $AB3,$

Wedge $AB4,$

$W_1=(6\frac{3}{2})19\mathrm{.}0=171\mathrm{.}0kN$

$W_2=(6\frac{6}{2})19\mathrm{.}0=342\mathrm{.}0kN$

$W_3=\frac{1}{2}2919\mathrm{.}0+342=513kN$

$W_4=\frac{1}{2}2919\mathrm{.}0+513=684kN$