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Geodesy, geomechanics and underground construction

Application of fractal dimension theory for the estimation of spatial variability of soil parameters

Michał Misciorak1
Grzegorz Janik2
  • 1 — Agriculture University of Wroclaw
  • 2 — Agriculture University of Wroclaw
Date submitted:
Date published:


This work aims to estimate stability of variograms used for estimation of spatial variability of moisture. The analysis is based on soil moisture measurement taken at the depth of 10 cmbelow the ground level. The research took place in Sucha Rzeczka town at warmińsko-mazurskie voivodeship, on the greenland. The research allowed to construct moisture variograms for N max  = 40 and to estimate fractal dimension. According to the measurements and analysis it has been ascertained that the stability of variograms is satisfying when they are constructed for at least 20 compared pairs of measurement points. The high value of fractal dimension D = 1,8 proves that the randomness of moisture in the examined area is high. Fractal dimension value stabilizes when it is estimated on the basis of variograms constructed for at least 30 compared points. 

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