A concrete retaining wall (unit weight 22.5 kN/m3) is to be checked for stability under seismic conditions. The wall has a rectangular cross section 6 m high and 1.5 m wide. The wall retains a...

A concrete retaining wall (unit weight 22.5 kN/m3) is to be checked for stability under seismic conditions. The wall has a rectangular cross section 6 m high and 1.5 m wide. The wall retains a cohesionless soil (unit weight of 17.5 , angle of internal friction of 33°). The foundation soil under the wall is similar. The backfill is sloped, extending upslope from the wall at an inclination of 30°. The wall is located in an area where the values of A_v
and A_a
equal 0.20. For this study, assume that the angle of the lateral earth force acts 16° from the horizontal (approximately half of the value of the angle of internal friction) and that k_v
is half of k_h.

(a) Determine the value of the earthquake active lateral pressure coefficient, KAE.

(b) The wall is located in an area where the backfill region is undeveloped so that the allowable wall displacement is 150 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.