The load arrives all at once, but the water cannot. Every bit of the load is first carried by the pore water, and the clay only settles as that water is squeezed out.
Each isochrone is the excess pore pressure left at one instant. It is pinned to zero at every drained face and bulges in the middle, where the water has furthest to travel.
Time enters only through T = cv·t/H²dr. Halve the drainage path and the same job is done in a quarter of the time, which is why a sand layer under the clay matters so much.
How much it settles and how fast are two separate questions. Cc, e0 and the stress change set the total, cv and the drainage path set only the rate.
Primary consolidation ends when the excess pore pressure has gone. Creep carries on afterwards at a steady amount per log cycle of time.