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

Abstract

This paper presents an easy-to-apply methodology that allows obtaining the permeability index and the initial hydraulic conductivity of clayey soils, basic constitutive parameters in non-linear models of consolidation, based on the laboratory oedometer test. For this, the data of the void ratio, compressibility index and characteristic consolidation time are taken from the test and, as an inverse problem, the constitutive permeability parameters sought are determined by applying the universal solutions of the characteristic time for a general non-linear consolidation model with constitutive relations void ratio-effective soil stress and hydraulic conductivity-void ratio of logarithmic type. The application protocol of the inverse problem is described in detail and illustrated by a series of applications carried out on real laboratory data belonging to two different soils. The influence that errors in laboratory parameter measurements can have on the final values of the permeability index and initial hydraulic conductivity is studied, showing the maximum deviations that may appear and, by last, the precision of the results obtained.

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.…”

Methodology to Obtain Universal Solutions for Systems of Coupled Ordinary Differential Equations. Examples of a Continuous Flow Chemical Reactor and a Coupled Oscillator

“…On the other hand, nonlinear consolidation models add a constitutive law for the variation of the hydraulic conductivity with the void ratio (which, in turn, is related to the soil effective stress by another different constitutive relationship). Therefore, by using the universal curves of characteristic time and average degree of settlement [21], it is possible to address an inverse problem [22] in which, from a simple oedometer test, we obtain the initial hydraulic conductivity of the soil sample as well as its variation during the consolidation process. At this point, it is important to note that in the oedometer test (based on the linear consolidation theory and normalized in ASTM D2435), it is only possible to obtain the soil compressibility curve (relationship between the void ratio and the effective stress) and consolidation time.…”

“…In this test, hydraulic potentials, flow rates, or evacuated water velocity are not measured, so hydraulic conductivity cannot be determined. However, the existence of universal curves for the non-linear problem and their use in an inverse methodology, based on the application of two successive load steps in the oedometer test, have allowed obtaining this property in a very precise way [22].…”

An Application of Inverse Problem and Universal Solutions for Pumping Wells in Unconfined Aquifers

“…Examples of problems that have been approached employing the discriminated nondimensionalization technique are flow under dams [13], solute and temperature flow [14] and soil consolidation [15]. In addition, this work is also an approach to an inverse engineering problem [16], as it aims to infer the value of some properties, in this case, the hydraulic horizontal and vertical conductivity values from measured variables that are unknown in directs problems (in these scenarios, pumping flow and seepage surface). The accuracy of the proposed methodology is presented, analyzing the influence of measure deviations of pumping flow and seepage surface on the precision of the sought parameters and affecting the variables by statistic errors of 0.5-2%.…”