GGU-CONSOLIDATE: Fundamentals

In complete analogy to the above relationships, a numerical solution can also be modelled with difference equations. In the system described in the figure in the previous chapter (non-cohesive layer - cohesive layer - non-cohesive layer), the numerical solution offers no advantages, as generally more time will be needed to model the results. The numerical solution of a consolidation problem can only show its undisputed advantages if a system with more than one layer is present and/or if there is a pore water pressure distribution that is not constant over the layer thickness. The relationships used for the solution are described in

• Braya M. Das (1983)
  ADVANCED SOIL MECHANICS
  McGraw-Hill

The derivations are therefore not repeated here.

Difference equations are applied to the depth distribution of the pore water pressures as well as to the time dimension. It is important to remember that the quality of the numerical solution is dependent upon the iteration size (small iterations = high precision but longer computing times). The depth distribution steps for pore water pressures (Δz) can be user-defined. The time dimension step Δt will be automatically selected by the program such that convergence is guaranteed. The following is valid after Das regarding the relationship of the normalised values Δz and Δt:

Δt / (Δz)² < 0,5

In the program, the stricter demand of 0.2 is implemented as opposed to 0.5.