Yes, it's 2 springs in parallel, so F=k1x1 + k2x2. Once the bottom spring (s2) disconnects, it's just one spring with F=k1x1. Note that F=0 on the bottom spring when it disconnects -- that is your x=0 point for that spring.

The restorative force as a function of distance will look like a ramp that suddenly becomes steeper when the second spring is acting.