Scale dependence of tortuosity in soils under contrasting cultivation conditions

Tortuosity is a parameter controlling flow and transport in soils. Under fully saturated and single-phase flow conditions, tortuosity depends not only on porosity but also on the sample volume (or dimension). However, most tortuosity models proposed in the literature ignore the effect of sample size. In this study, we address the scale dependence of tortuosity in soils under two cultivation conditions: conventional tillage (CT) and no tillage (NT). We apply a theoretical model linking tortuosity to porosity (ϕ), critical porosity (ϕc), some fundamental length scale (C), and optimal path fractal dimension (Dopt). To evaluate the theory, we compare theoretical estimations with tortuosity values measured on X-ray microcomputed tomography images of various linear sizes from L = 736.8–36,887.7 µm on 12 soil samples. We demonstrate that the proposed approach accurately estimates the scale dependence of tortuosity in soils. We also find that the theoretical estimations are more accurate for the CT samples than the NT ones. The accuracy of the proposed model is also compared to that of another model derived by assuming that a porous medium consisted of two-dimensional square solid particles. We find that the percolation-based theoretic model estimates tortuosity more precisely than the other model. Our results show that the effect of scale on tortuosity is more profound for the NT samples than the CT ones. •We propose a theory to estimate scale-dependent tortuosity in soils.•The proposed theory is evaluated using 24 datasets.•The proposed approach accurately estimates the scale dependence of tortuosity.•Theoretical estimations are more accurate in the CT samples than the NT ones.•Effect of scale on tortuosity is more profound in the NT samples than the CT ones.