Dimensionless characterization of the non-linear soil consolidation problem of Davis and Raymond. Extended models and universal curves

Abstract

The dimensionless groups that govern the Davis and Raymond non-linear consolidation model, and its extended versions resulting from eliminating several restrictive hypotheses, were deduced. By means of the governing equations nondimensionalization technique and introducing the characteristic time concept, both in terms of settlement and pressures, was obtained (for the most general model) that the average degree of settlement only depends on the dimensionless time while the average degree of pressure dissipation does it, additionally, on the loading ratio. These results allowed the construction of universal curves expressing the solutions of the unknowns of interest in a direct and simple way.

Understanding Complex Traffic Dynamics with the Nondimensionalisation Technique

“…The procedure for the nondimensionalisation of differential equations is well known and thoroughly explained in the literature [23,24]. Moreover, it has been successfully applied to a wide range of non-linear problems, such as diffusion of chlorides in reinforced concrete structures or soil consolidation [25][26][27][28], where the universal curves obtained offer invaluable information about the problems considered while offering a significant reduction in computational time with a minimal increase in error. In this article, we tackle the problem of understanding the involved behaviour of traffic by searching for the universal curves in a complex traffic model.…”

Method to Determine the Constitutive Permeability Parameters of Non-Linear Consolidation Models by Means of the Oedometer Test

“…Recently, the dimensionless groups that characterize the aforementioned models, as well as their extensions to more general and precise formulations obtained from the elimination of several restrictive hypotheses [11], have been derived from their governing equations and the application of the pi theorem [12], which has allowed the construction of universal curves of easy use for the determination of the characteristic consolidation time, the average degree of pressure dissipation and the average degree of settlement [13][14][15][16]. The results obtained by these authors reduce the numerous coefficients (dimensional or not) involved in the models to a small number of dimensionless groups based on which the solution for each unknown is presented by a single universal curve.…”