Fractal scaling of surface roughness in artificially weathered smectite-rich soil regoliths

Abstract Laboratory trials were established to simulate, under controlled conditions, the natural weathering sequence of smectite-rich soil regoliths from a highly degraded badland area at Vallcebre, Eastern Pyrenees Range (Spain). Experiments were carried out to deepen the knowledge on the response of the bulk materials to experimental freezing–thawing and wetting–drying cycles, and the role of the mineral components in the path of surface structure detachment. During the experiments, variation of surface roughness was determined by measuring consecutive transects of the artificially weathered samples with a noncontact laser profile meter and data were analysed with a program written for this purpose. The analysis of data was based on the calculation of the fractal dimension, according to the Richardson equation, of sequential surface profiles of samples in frozen, thawed, wetted and dried conditions in order to achieve a dynamic description of surface aggregate shape arrangement along the whole sequence and at different scale ranges. The Hurst exponent of selected bulk data was also calculated in order to find added evidence of the nature of surface, which, in some cases, appeared to be multifractal with the Richardson diagram. The fractal model applied allowed to obtain fractal dimension values of surface roughness which were used to explain how the pedological characteristics of a given material containing clay and carbonate association may react to applied climatic extremes, thereby showing differential surface arrangement and weathering paths. Freezing and thawing as well as wetting and drying events modified the sample's surface, and these effects describe the material susceptibility to weathering against individual climatic components and may be useful in erosion modelling at the catchment scale.

[1]  L F Richardson,et al.  The problem of contiguity : An appendix to statistics of deadly quarrels , 1961 .

[2]  J. Y. Lorendeau,et al.  AN AUTOMATED, NONCONTACT LASER PROFILE METER FOR MEASURING SOIL ROUGHNESS IN SITU , 1990 .

[3]  H. KUIPERS,et al.  A reliefmeter for soil cultivation studies. , 1957 .

[4]  F. Plana,et al.  How mudrock and soil physical properties influence badland formation at Vallcebre (Pre-Pyrenees, NE Spain) , 1992 .

[5]  J. Oades.  Soil organic matter and structural stability: mechanisms and implications for management , 1984 .

[6]  John W. Crawford,et al.  On the relation between number-size distributions and the fractal dimension of aggregates , 1993 .

[7]  D. Regüés,et al.  Regolith behaviour and physical weathering of clayey mudrock as dependent on seasonal weather conditions in a badland area at Vallcebre, Eastern Pyrenees , 1995 .

[8]  J. R. Smith,et al.  Coordinate systems and map projections , 1973 .

[9]  D. R. Linden,et al.  Parameters for Characterizing Tillage-induced Soil Surface Roughness1 , 1986 .

[10]  A DIGITAL SURFACE-ROUGHNESS METER , 1994 .

[11]  E. Perfect,et al.  Unbiased estimation of the fractal dimension of soil aggregate size distributions , 1994 .

[12]  Azer Bestavros,et al.  Explaining World Wide Web Traffic Self-Similarity , 1995 .

[13]  Cameron D. Grant,et al.  Roughness of soil fracture surfaces as a measure of soil microstructure , 1990 .

[14]  Garrison Sposito,et al.  Fractal Fragmentation, Soil Porosity, and Soil Water Properties: I. Theory , 1991 .

[15]  B. H. Kaye.  Specification of the ruggedness and/or texture of a fine particle profile by its fractal dimension , 1978 .

[16]  D. Regüés,et al.  Structure and porosity of smectitic mudrocks as affected by experimental wetting—drying cycles and freezing—thawing cycles , 1996 .

[17]  B. Mandelbrot.  How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension , 1967, Science.

[18]  F. Plana,et al.  Laser elevation measurements of a smectite-rich mudrock following freeze-thawing and wet-drying cycles , 1995 .

[19]  Pardini,et al.  A combination of laser technology and fractals to analyse soil surface roughness , 1998 .