An investigation into sources of soil crack heterogeneity using fractal geometry

Fractal dimensions were used to quantify the complex geometry of soil cracking patterns. Two fractal dimensions were measured to provide an adequate description of soil cracks: the mass fractal dimension, D-M (which provides a measure of crack heterogeneity) and the spectral dimension, d (which provides a measure of crack connectivity). The cracking patterns generated by four soils were compared and related to their textural characteristics. As the clay content of the soil increased (6.1%-24.3%), so did D-M (1.29-1.43), and d (1.03-1.33). Correlations indicated that there was a significant (P < 0.01) linear relation between the soil's clay content and the D-M and d of cracks, the correlation coefficients obtained being equal to 0.965 and 0.840, respectively. Significant correlations (P < 0.01) were also observed between structural stability indices of the soil and the fractal dimensions of its cracks, increases in the stability of the soil, particularly of the clay fraction, being associated with cracks with greater fractal dimensions.