So, I've been looking further to my problem, and I think I might have found a bug...
In sisyphe.F, the call of TASSEMENT updates "ES", but not "ES_VASE". So, at the next time step, when calling SUSPENSION_MAIN, the line 445
ES(I,J) = ES_VASE(I,J)
brings back the initial values to each layer thickness. So, at each time step, the same amount of mud is transferred to the beneath layer, overestimating consolidation.
Adding the lines
DO I = 1, NPOIN
DO J = 1, NOMBLAY
ES_VASE(I, J) = ES(I, J)
ENDDO
ENDDO
after the call to TASSEMENT in sisyphe.F seems to solve the problem. But I guess it is not the optimal solution.
I would be happy if someone could cross check my solution.