The statistical relationship between unconfined compressive strengths and the frequency distributions of slope gradients — A case study in northern Hungary

This paper focuses on the question of whether there is a deterministic connection between the slope gradient and unconfined compression strength (UCS) as a lithological factor and on describing the nature of this connection. Moreover, the authors determined the sensitive statistical parameters in the statistical surface analyses. The surface analyses were carried out in an area extending over 1500 km2 in northern Hungary and containing parts of the uplifted Palaeozoic and Mesozoic basement and the semi-consolidated material of the Palaeogene and Neogene molasse sediments. geological formations of the area were grouped into 10 petrophysical categories characterised by unconfined compressive strength as a petrophysical parameter. The geological database was the digitalized geological map of North Hungarian Region (1 : 100 000). The digital topographic database was based on 10 m contour lines of 1 : 50 000 maps, the digital elevation model was generated by kriging interpolation. Three topographic models were created with resolutions of 25 × 25, 50 × 50 and 100 × 100 m per pixels. t correlation can be shown between the UCS and the relative frequency of the slope gradient. The adequate regression procedure is the power regression for low slope category values while logarithmic regression is applicable at high slope angles. Based on the characteristic of the relationship and the value of r2, slope category intervals can be identified the relative frequency of which is proven to be determined by the UCS. These intervals are found to be between 4–10%, 10–16%, 16–22%, 22–44% and over 44%. the determination equations of slope gradient between 4–10% and over 44%, the UCS of the bedrock can be calculated approximately as the average value of the two calculated results. So the quotient of the frequency of these two category intervals can be regarded as an important morphometric index for a given bedrock. he aspect of petrophysical characteristics, the rock with UCS between 6 and 86 MPa were proven to be deterministic for the slope development i.e. in the determination of the slope category frequencies. Applying the relative frequency of slope gradients a relative erosion resistance of the petrophysical categories can be calculated. ering the determination coefficients, among the statistical parameters of the distribution of slope category values the standard deviation, mode, mean and median proved to be determined by the UCS of the bedrock.