Use of multifractal parameters to determine soil particle size distribution and erodibility of a physical soil crust in the Loess Plateau, China

• Structural and depositional crusts have variable particle size distribution ( PSD ). • PSD is measured under different rainfall durations to determine soil erodibility. • The formation mode and PSD of physical crust depend on micro terrain and rainfall. • Rainfall and tillage result in heterogeneous PSD and erodibility. • Significant correlations are found between erodibility and multifractal parameters. Understanding the knowledge of multifractal analysis on particle size distribution ( PSD ) of soil physical crusts is indispensable for progressing soil surface erosion mode. In this study, hoeing tillage (20 cm long × 15 cm wide × 5 cm deep) were conducted to simulate classic tillage mode in Yangling, China to obtain physical crusts under artificial rainfall (60 mm h −1 intensity with three durations (5, 15, and 30 min)). We defined crusts formed in ridges as structural crust ( C st ), formed by infiltration of runoff in hoes as sediment-containing depositional crust ( C scd ), and formed by the extraction of runoff as sediment-free depositional crust ( C sfd ). Soil stratification methods were used to explore physical crust particle sorting. Results represented that the sand content of C st , C scd , and C sfd decreased, whereas clay and silt contents increased after rainfall compared to undisturbed soil. There was no significant difference between C scd and C sfd under short rainfall duration. Three crust types became gradually concentrated in areas with higher density with increasing rainfall duration according to six common parameters in the generalised dimension spectrum ( D 0 , D 1 , D 2 , D 1 / D 0 , D v ( D -10 – D 0 ), and D s ( D 0 – D 10 )). Multifractal singularity spectrum ( α 0 , A v , F v ) showed that PSD was most symmetrical in C sfd , followed by C scd and C st . Erodibility index K EPIC was largest for C st , followed by C sfd then C scd . The relationship between K EPIC and multifractal parameters were significant. Spatial difference caused by tillage activities and rainfall events determine the heterogeneous formation mode, particle size distribution and erodibility of physical crust.