Is A concrete retaining wall (unit weight 22.5 $\mathrm{kN} / \mathrm{m}^3$ ) is to be checked for stability under seismic conditions. The wall has a rectangular cross section $6 \mathrm{~m}$ high and $1.5 \mathrm{~m}$ wide. The wall retains a cohesjonless soil (unit weight of $17.5 \mathrm{kN}=\mathrm{m}^3$, angle of internal friction of $33^{\circ}$ ). The foundation soil under the wall is similar. The backfill is sloped, extending upslope from the wall at an inclination of $30^{\circ}$. The wall is located in an area where the values of $A_c$ and $A_e$ equal 0.20 . Fer this study, assume than the angle of the lateral earth force acts $16^{\circ}$ from the horizontal (approximately half of the value of the angle of internal friction) and that $k_r$ is half of $k_{\text {lir }}$.
(a) Determine the value of the esrthquake active lateral pressare coefficient, $\boldsymbol{K}_{A R}$ :
(b) The wall is located in an area where the backfill region is undeveloped so that the allowable wall displacement is $150 \mathrm{~mm}$. What weight of wall should be provided to have a factor of safety against sliding equal to 1.25 ?
(c) Determine the factor of safety against overturning for this earthquake condition (ref. Figure 31 for position of lateral forces). Assume that the foundation soils are adequately compact so that liquefaction during earthquake will not occur.