Use of discriminated nondimensionalization in the search of universal solutions for 2-D rectangular and cylindrical consolidation problems

Abstract

The solution to the 2-D consolidation problem, both for rectangular and cylindrical domains, has been widely studied in the scientific literature, reporting the most precise solutions in the form of analytical expressions difficult to handle for the engineer due to the high number of parameters involved. In this paper, after introducing a precise definition of the characteristic time, both this magnitude and the average degree of consolidation are obtained in terms of the least number of dimensionless groups that rule the problem. To do this, the groups are firstly derived from the dimensionless governing equations deduced from the mathematical model, following a discriminated nondimensionalization procedure which provides new groups that cannot be obtained by classical nondimensionalization. By a large number of numerical simulations, the dependences of the characteristic time and the average degree of consolidation on the new dimensionless groups have allowed to represent these unknowns graphically in the form of universal curves. This allows these quantities to be read with the least mathematical effort. A case study is solved to demonstrate the reliability and accuracy of the results.