An existing roadside embankment needs to be reinforced using

geogrid sheets. The embankment is 15-m high and the slope angle

is 40°. The in situ soil will be used as the reinforced backfill. The

soil strength parameters are f = 220 and c = 15 kN∕m² in both the

embankment and foundation sections. The unit weight is 17.3 kN∕m³.

The critical failure surface is assumed to be a toe circle, and the center

is located at (+3 m, +18 m) with respect to the toe at (0,0). Assume

the groundwater table is far below the foundation. The ultimate

tensile strength of the geogrid is 75 kN∕m. The vertical spacing is

chosen to be 40 cm. For the critical failure circle, how many layers of

geogrid are required to raise the factor of safety to 1.4?