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Purpose is to analyze distribution of granulometric composition of tuff as well as ultimate composition and identify dependence of its softening in the process of water saturation based upon a set of experiments to assess raw materials importance of the mineral. Methods. Laboratory experiments were carried out to determine ultimate composition of tuff extracted from different open pits of the region. Methods of mathematical statistics were applied to derive analytical dependences describing the tuff softening in the process of water saturation. The dependences denote logarithmic nature of the saturation increase along with the increase in the sample weight. Findings. It has been determined that tuff is a valuable mineral rather than basalt extraction waste. Thus, tuff needs both mining and complex approaches for processing and extracting of useful metals and silicates. Analytical dependences of tuff softening during water saturation have been defined. The dependences denote logarithmic nature of the saturation increase based upon a sample weight increment. Magnetic susceptibility of tuff, turned on magnetic field induction, has been identified. Dependences of distribution of technological indices (i.e. product yield, copper content and yield) in terms of granulometric-size class have been identified; the basic factors for crushing process have been determined; and regression dependences of grinder efficiency upon the input factors have been derived. Regression model of a crushing process of a general technological scheme of ore processing has been obtained involving the initial fragmentation using a jaw crusher, and additional fragmentation (i.e. reduction) using a sizer. Originality.It has been determined that magnetic susceptible tuff share is 49% of the sample weight; the remaining part is a silicate share. Logarithmic nature of the analytical softening dependences while water saturating has been identified. The above-mentioned denotes the increased saturation along with the increase in a sample weight. Practical implications. The definition of tuff ultimate composition as well as analytical softening dependences in the process of water saturation makes it possible to calculate the required water consumption. Keywords: tuff, basalt, softening, water saturation, silicate, magnetic susceptibility, ultimate composition, crushing

This paper deals with a nonlinear soil moisture transport problem, solved with addition of satellite observed soil moisture. The satellite data are assimilated into the model using Newtonian nudging method. Evaluation is done by the triple collocation method, which involves three independent data sources: model results, ground stations and ERA5 climatic data. The results testify that model results are nearly as accurate as the ground station measurements.

Soil environments are heterogeneous in their nature. This heterogeneity creates significant difficulties both in terms of construction practice and in terms of the mathematical modeling and computer simulation of the physical-chemical processes in these heterogeneous soil arrays. From the standpoint of mathematical modeling, the issue is the discontinuity of functions, which characterize the examined processes, on such inclusions. Moreover, the characteristics of such inclusions may depend on the defining functions of the processes studied (head, temperature, humidity, the concentration of chemicals, and their gradients). And this requires the modification of conjugation conditions and leads to the nonlinear boundary-value problems in heterogeneous areas. That is why this work has examined the impact of the existence of thin inclusions on the conjugation conditions for the defining functions of the filtration and geomigration processes on them. The conjugation condition for heads has also been modified while the mathematical model of an elastic filtration mode in a heterogeneous array of soil, which contains thin weakly permeable inclusions, has been improved. The improvement implies the modification of conjugation conditions for heads on thin inclusions when the filtering factor of the inclusion itself is nonlinearly dependent on the head gradient. The numerical solution to the corresponding nonlinear boundary-value problem has been found using a finite-element method. A series of numerical experiments were conducted and their analysis was carried out. The possibility of a significant impact on the head jump has been shown taking into consideration the dependence of filtration characteristics of an inclusion on head gradients. In particular, the relative difference of head jumps lies between 26% and 99% relative to the problem with a stable filtration factor for an inclusion. In other words, when conducting forecast calculations, the influence of such dependences cannot be neglected

The use of low-temperature heat of industrial and natural origin for heating the soil in greenhouses allows practitioners to get very early vegetable and berry crops. The paper suggests a mathematical model of greenhouse heat exchange with a system of soil surface heating for substantiating the system structure and its efficiency in different conditions. The solution of the mathematical model was performed using the method of least squares in COMSOL Multiphysics software. The comparison of the results of experimental studies with the results of mathematical modelling revealed that the proposed mathematical model with a high degree of reliability allows predicting the thermal regime in greenhouses with surface soil heating using cover sleeves.

In this paper we study a mathematical model of soil moisture transport with variable porosity. The problem is set for the case of highly concentrated solute spilled onto soil surface. We investigate the way solute transfer, adsorption of contaminant by soil particles and variable porosity influence infiltration of solute into the soil profile. For that purpose, two models are used: a classical one and the one with consideration of mentioned factors. By comparing the results of both models, we established that high concentration of solute causes moisture transport to transpire more slowly, and the pollutant to remain on the soil surface for longer time. Numerical results indicate that porosity can vary considerably under the conditions of intensive contamination with salts.

Mathematical modeling and computer simulation methods have been used to investigate the extent of influence exerted by bio-clogging on the dynamics of excess head scattering in the soil massif. To this end, the classical equation of filtration consolidation has been modified for the case of variable porosity resulting from changes in the biomass. The numerical solution to the constructed mathematical model in the form of a nonlinear boundary problem was derived by a finite-element method. Numerical experiments were carried out and their analysis was performed. Specifically, this paper shows the charts of pressure differences in the soil array when neglecting bio-clogging and when estimating the effects exerted by bio-clogging at specific points in time. The numerical experiments demonstrated that in two years after the onset of the consolidation process in the neighborhood of the lower limit of the examined soil mass with a thickness of 10meters, excess heads fall from the initial value of 10m to 4m. The greatest impact from the clogging of pores by microorganisms is revealed in the neighborhood of an upper limit. At a depth of 1 m, at t=180 days, the pressure difference reaches 2.4m. This is about 200% of the pressure distribution without taking into account the effects of bio-clogging. Over time, the effect of bacteria on the distribution of pressures in the neighborhood of the upper boundary decreases. However, this effect extends to the entire soil mass, up to the lower limit. Thus, at t=540 days, at the lower limit, the effect of bio-clogging leads to that excess heads are 1.8 m greater than for the case of pure water filtration (a relative increase of about 80%). Bio-clogging processes are intensified as a result of the development of microorganisms when organic chemicals enter the porous environment. Therefore, from a practical point of view, studying them is especially relevant for household waste storage facilities and the stability of their soil bases. It is advisable to undertake research by using the methods of mathematical modeling and computer simulation

The mathematical model of filtering with regard to colmatation and suffusion in the system bioplato-filter 2. This saturated porous medium is considered in terms of a complex heterogeneous system "fill"-"concentration of pollutants in porous liquid-concentration of colmatating particles. Vzaêmovplivi system parameters are taken into account through: 1) the dynamic change of the porosity of the backfill in the process of filtering; 2) nonlinear dependence coefficient filter porosity of backfill; 3) dependence of velocity of filtration coefficient of filtering and gradient heads, and hence – and porosity. Taking into account the following interplays allowed to increase the adequacy of mathematical models for the study of physical processes, however, led to the necessity of the study of nonlinear boundary value problems for systems of differential equations in partial derivatives. Nonlinearity of the boundary value problem does not allow to speak about her analytical solutions. Numerical solutions of the problems found by the method of finite elements with a software implementation of the relevant algorithms in FreeFem ++. Computer modeling showed that when taking into account nonlinear dependence coefficient of filtration from the concentration of colmatating particles and dynamic changes of porosity in the process of filtering, predictive performance bioplato for six months reduced by 25 % . Therefore, it is necessary to develop engineering solutions for reducing the influence of the colmatation-suffusion processes on the processes of filtering. The forecasting work bioplato relevant conduct on the design stage in order to implement predictive calculations. It is done by means of mathematical and computer modeling

This paper presents the research results of the pulp movement process along the extraction chamber bottom to the suction pipe of the pulp lifting device in case of downhole hydraulic mining the volcanic tuff-stone. The washout process and hydraulically operated transportation of the tuff-stone hydraulic mixture, when forming the extraction chamber, have been studied under various conditions and methods of exposure. As a result, the dominant parameters have been determined influencing the hydrodynamic washout technology as well as tuff-stone hydraulic mixture lifting to the alluviation map. The dependences have been substantiated of the washout process performance and transportation capacity of the hydraulic mixture flow on the determined parameters. To calculate the process of pulp flow-over along the extraction chamber bottom to the intaking hydraulic elevator headwall, the systems of equations have been determined based on the modelling the movement of tuff-stone hydraulic mixture along the extraction chamber bottom during hydraulic washout. The dependences of the contact strength of the tuff-stone samples mined by downhole method on the time spent in water are presented, resulting in determination of the tuff-stone weakening coefficient and the degree of its saturation with water.

The problem of pollution transfer by water flow in open channel was considered. The mathematical model of the problem was constructed. The numerical solution of the onedimensional boundary problem was obtained. The computational algorithm for solving the problem was programmed to implement. A series of numerical experiments with their further analysis was conducted.