A New Model for Solving Hydrological Connectivity Inside Soils by Fast Field Cycling NMR Relaxometry

In this paper, a new quantitative approach for estimating the structural and functional connectivity inside soil by Fast Field Cycling (FFC) NMR relaxometry is presented, tested by measurements carried out in three samples with different texture characteristics. Measurements by FFC NMR relaxometry have been carried out using water-suspended samples and Proton Larmor frequencies (νL) ranging in the 0.015–35 MHz interval. Two non-degraded soil samples, with different textural characteristics, and a degraded soil collected in a badland area, were analyzed. For a given soil and any applied Proton Larmor frequency, the distribution of the longitudinal relaxation times, T1, (i.e., relaxogram) measured by FFC NMR has been integrated, and the resulting S-shaped curve (i.e., relaxogram integration curve) was represented, for the first time, by Gumbel’s diagram. This new representation of the relaxogram integration curve, transforming the S-shaped curve into a straight line, allowed for distinguishing three linear components, corresponding to three different relaxation time ranges, characterized by three different slopes. Two points, identified by the abrupt slope changes of the relaxogram integration curve plotted in Gumbel’s diagram, are used to identify two characteristic values of relaxation time, T1A and T1B, which define three well-known pore size classes (T1 < T1A micro-pores, T1A < T1 < T1B meso-pores, and T1 > T1B macro-pores). The relaxogram integration curve allowed for calculating the non-exceeding empirical cumulative frequency, F(T1), corresponding to the characteristic T1A and T1B values. The analysis demonstrated that the relaxogram can be used to determine the pore-size ranges of each investigated sample. Finally, using the slope values of the three components of the relaxogram integration curve, a new definition of the Structural Connectivity Index, SCI, and Functional Connectivity Index, FCI, was proposed.