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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

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