Eesti liiva- ja kruusavarude lõimise matemaatiline teisendusmeetod üleminekuks uutele riiklikult kehtestatud nõuetele [Magistritöö. Juhendajad: K. Urtson ja R. Hints]

On 22.12.2018 a new mineral exploration procedure was adopted in Estonia and the new requirements for the registration of sand and gravel as mineral resources began to apply. Prior to that gravel was considered to be mineral resource when sediments contained more than 35% of the particles with diameter > 5 mm and sand was classified as a mineral resource containing more than 35% of the particles with diameter < 5 mm. But in the new mineral exploration procedure, gravel is redefined as a mineral resource where more than 35% of the particles should have larger diameter than 31,5 mm and for sand the same parameter needs to be less than 35%.

Before the new mineral exploration procedure the grain size analyses of sand and gravel resources was carried out according to standard GOST 12536, but now to fullfill the new requirements the standard of EVS-EN 933-1 needs to be adapted. Two standards use different sieve sets. New regulations have put mining companies into a difficult situation, where the requirements for resource classification have changed significantly, but the material names and the mining rights fee have not been changed. The fees depend on the usage of the mineral resources which is determined by the sieves. Making new geological surveys in quarries and miners would be expensive and time consuming, therefor companies would prefer alternative cheaper and faster options such as mathematical conversion of existing grain size data according to new standards.

The goal of the master's thesis was to find reliable mathematical method for conversion of the grain size data obtained according to GOST 12536 standard to the grain size data which are in agreement with EVS-EN 933-1 standard. For this purpose, 99 samples representing different particle size distributions and genetic types were collected from different quarries across Estonian mainland. The samples were sieved using both standards - GOST 12536 and EVS-EN 933-1.

The obtained grain size distributions where characterized by means of moment method for mapping principle grain size distribution variations within considered dataset.

The linear and loglinear interpolation methods were tested as possible solutions for estimating grain size distribution applicable to EVS-EN 933-1 based on measured GOST 12536 grain sizes values. The methods were selected due to their wide usage and simplicity. To evaluate the accuracy of estimated values and suitability of used interpolations the estimation errors between calculated grain size values and real measured values according to EVS-EN 933-1 standards were found. Obtained mean errors were smallest in case loglinear interpolation, which used log10 cumulative percentage of grain size fraction for calculations. However, the mean errors were not uniformly distributed and remained considerably high for some small grain size fractions. Therefor linear and loglinear interpolation methods were found to be inaccurate procedures for recalculations of grain size data.

The thesis proposes other options for converting grain size data of Estonian sand and gravel deposits. One of those options is similarity method, which requires a large database of grain size data. Also the spline and the Gompertz curve method may give the better results for solving existing problem. Nevertheless, those methods are more sophisticated compared to linear models.