Spatial distribution of soil penetration resistance as affected by soil compaction: The fractal approach

Using semivariograms and fractal dimension (D), we identified the spatial variation of penetration resistance (PR) in variously compacted silty loam in the Lublin region, South-East Poland. Four compaction treatments were as follows: zero traffic (0p), one pass of tractor (1p), three passes of tractor (3p), and (8p) eight passes. Penetration resistance was measured in a square net of 0.6 m × 0.6 m with grid density of 0.05 m, in horizontal planes at depths of 0.05, 0.15, 0.25, 0.35, 0.45 and 0.55 m in each traffic treatment. The data were analysed in 6 horizontal planes and 12 vertical planes. The vertical planes were obtained by transforming the measured data along one side of the square at every 0.05 m. Total number of penetrations was 864. Fractal dimension (D) was estimated from the slope of the log–log semivariogram plots. The semivariograms showed spatial autocorrelation of penetration resistance in the horizontal and vertical planes. Direction in space was important in this study. In the horizontal planes the differentiation of penetration resistance semivariance at different depths was considerable and not clearly related with traffic intensity. In the vertical planes the semivariograms showed spatial dependence of the PR and evident decreasing of semivariance with increasing traffic intensity. Kriging-interpolated maps revealed that the differentiation of penetration resistance was higher in the vertical than in the horizontal planes. The vertical differentiation was higher in 0p than in the remaining treatments. The overall mean fractal dimensions in the vertical planes increased with increasing compaction levels and can be a useful indicator of the compaction level. The opposite courses of fractal dimension in the vertical and horizontal planes indicate spatial anisotropy in distribution of penetration resistance.