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A $6$ m high retaining wall having a smooth vertical back face retains a layered horizontal backfill. Top $3$ m thick layer of the backfill is sand having an angle of internal friction. $\phi = 30^{\circ}$ while the bottom layer is $3$ m thick clay with cohesion, $c=20$ kPa. Assume unit weight for both sand and clay as $18 \: kN/m^3$. The total active earth pressure per unit length of the wall (in kN/m) is:

  1. $150$
  2. $216$
  3. $156$
  4. $196$
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