The influence of the biocolmation of the geobarrier for organic waste storage on the values of head drops has been investigated. A mathematical model of filtration of organic substan ces taking into consideration the biocolmation effect was formed. The mathematical model contains the equation of filtration under conditions of variable porosity. In addition, the mathematical model includes the equation of transfer of organic chemical substances in pore fluid and the equation of dynamics in bacteria biomass in a porous medium based on the Monod equation. The problem in the region with a thin inclusion was solved by the method of finite elements. The schematic algorithm of finding an approximate solution of the boundary problem, including the scheme of discretization over time, is presented. Numerical experiments were conducted with an analysis of their results. In particular, the tables have been given of the values of heads and their drops on inclusions when biocolmation is neglected and the values of heads and their drops on inclusions while taking into account biocolmation at specific moments of time. The numerical experiments showed that the existence of microorganisms in soil pores significantly influences the values of heads at the top and at the bottom of a geobarrier. In particular, relative changes in head drops, in comparison with the case of disregarding the influence of microorganisms, can reach 54.8 % towards an increase. Such differences, in turn, lead to a change in the estimation calculations of the propagation of waste storage contamination into groundwater. They can also cause negative changes in the stressed-strained state of a soil array in the vicinity of a geobarrier as a type of a thin inclusion and lead to the intensification of shear processes. At the same time, due to the nonlinearity of influences and complex interdependence among processes, it is not possible to predict such values and their differences without computer simulation and mathematical modeling

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The distribution of an organic chemical and the filtration process in the soil which contains a thin geochemical barrier are considered. Microorganism colonies develop in the presence of organic chemicals in the soil which leads to the so-called phenomenon of bioclogging of the pore space. As a result, the conductivity characteristics of both the soil as a whole and the geochemical barrier change. Conjugation conditions as a component of the mathematical model of chemical filtration in the case of inhomogeneity of porous media and the presence of fine inclusions were modified for the case of bioclogging. The numerical solution of the corresponding nonlinear boundary value problem with modified conjugation conditions was found by the finite element method. The conditions of the existence of a generalized solution of the corresponding boundary value problem are indicated. The results on the theoretical accuracy of finite element solutions are presented. Differences in the value of pressure jumps at a thin geochemical barrier were analyzed for the case considered in the article and the classical case on a model example of filtration consolidation of the soil in the base of solid waste storage. The excess pressure in 600 days after the start of the process reaches 25 % of the initial value when taking into account the effect of bioclogging, while is only 6 % for the test case disregarding the specified effect.

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

Побудовано математичну модель фільтра-ційної консолідації тіла греблі з водоводом і зоною вимиву в двовимірному випадку. Враховано вплив техногенних факторів. Розроблено комп'ю-терну програму для автоматизації розрахун-ків чисельного розв'язання крайової задачі без-сітковим методом радіальних базисних функцій. Проведено ряд числових експериментів і здійсне-ний їх аналіз Ключові слова: гідроенергетика, проблема фільтраційної консолідації, осмотичні явища, вільна поверхня, об'єктно-орієнтоване програ-мування Построена математическая модель фильтра-ционной консолидации тела плотины с водово-дом и зоной размыва в двумерном случае. Учтено влияние техногенных факторов. Разработана компьютерная программа для автоматиза-ции расчетов численного решения краевой зада-чи беcсеточным методом радиальных базисных функций. Проведен ряд числовых экспериментов и осуществлен их анализ Ключевые слова: гидроэнергетика, проблема фильтрационной консолидации, осмотические явления, свободная поверхность, объектно-ори-ентированное программирование UDC 519.61/.64:627.05

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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 10 meters, excess heads fall from the initial value of 10 m to 4 m. 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 2.4 m. 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

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