A mathematical model of filtration consolidation of an inhomogeneous soil mass was formed taking into account the change in the size of the area during the compaction process. The inhomogeneity is considered as the presence of fine inclusions (geobarriers) the physical and mechanical characteristics of which differ from those of the main soil. From a mathematical viewpoint, the model is described by a one-phase Stefan problem that has a kinematic boundary condition on the upper moving boundary as its component. The purpose of the research is to find out the effect of fine inclusion on the dynamics of subsidence of the soil surface in the process of compaction. The change in the dimensions of the solution area is physically determined by the change in the volume of the pores of the porous medium in the process of dissipating excess pressure. If the permeability of the geobarrier is low, it affects the dynamics of consolidation processes and, accordingly, the magnitude of subsidence. Finite element solutions of the initial-boundary value problem for the nonlinear parabolic equation in the heterogeneous region with the conjugation condition of non-ideal contact were found. Numerical time discretization methods, a method for determining the change in the position of the upper boundary at discrete moments of time, and an algorithm for determining the physical and mechanical characteristics of a porous medium depending on the degree of consolidation are given. A number of test examples were considered, and the effect of a thin inclusion on the dynamics of the change in the position of the upper boundary of the problem solution area was investigated.

- Xiao T., Ni P., Chen Z., Feng J., Chen D., Mei G. A semi-analytical solution for consolidation of ground with local permeable pipe pile. Computers and Geotechnics.
**143**, 104590 (2022). - Vlasyuk A. P., Martynyuk P. M., Fursovych O. R. Numerical solution of a one-dimensional problem of filtration consolidation of saline soils in a nonisothermal regime. Journal of Mathematical Sciences.
**160**(4), 525–535 (2009). - Masum S. A., Zhang Z., Tian G., Sultana M. Three-dimensional fully coupled hydro-mechanical-chemical model for solute transport under mechanical and osmotic loading conditions. Environmental Science and Pollution Research.
**30**(3), 5983–6000 (2023). - Jozefiak K., Zbiciak A., Brzezinski K., Maslakowski M. A Novel Approach to the Analysis of the Soil Consolidation Problem by Using Non-Classical Rheological Schemes. Applied Sciences.
**11**(5), 1980 (2021). - Ding P., Xu R., Zhu Y., Wen M. Fractional derivative modelling for rheological consolidation of multilayered soil under time-dependent loadings and continuous permeable boundary conditions. Acta Geotechnica.
**17**(6), 2287–2304 (2022). - Bekele Y. W. Physics-informed deep learning for one-dimensional consolidation. Journal of Rock Mechanics and Geotechnical Engineering.
**13**(2), 420–430 (2021). - Bulavatsky V. M., Bohaienko V. O. Some Consolidation Dynamics Problems within the Framework of the Biparabolic Mathematical Model and its Fractional-Differential Analog. Cybernetics and Systems Analysis.
**56**, 770–783 (2020). - Li L., Qin A., Jiang L. Semi-analytical solution for one-dimensional consolidation of a two-layered soil system with unsaturated and saturated conditions. International Journal for Numerical and Analytical Methods in Geomechanics.
**45**(15), 2284–2300 (2021). - Chui Y., Martyniuk P., Kuzlo M., Ulianchuk-Martyniuk O. The conditions of conjugation in the tasks of moisture transfer on a thin clay inclusion taing into account salt solutions and themperature. Journal of Theoretical and Applied Mechanics, Sofia.
**49**(1), 28–38 (2019). - Ulianchuk-Martyniuk O. V. Numerical simulation of the effect of semi–permeable properties of clay on the value of concentration jumps of contaminants in a thin geochemical barrier. Eurasian Journal of Mathematical and Computer Applications.
**8**(1), 91–104 (2020). - Ulianchuk-Martyniuk O. V., Michuta O. R. Conjugation conditions in the problem of filtering chemical solutions in the case of structural changes to the material and chemical suffusion in the geobarrier. JP Journal of Heat and Mass Transfer.
**19**(1), 141–154 (2020). - Ulianchuk-Martyniuk O. V., Michuta O. R., Ivanchuk N. V. Finite element analysis of the diffusion model of the bioclogging of the geobarrier. Eurasian Journal Of Mathematical and Computer Applications.
**9**(4), 100–114 (2021). - Michuta O. R., Martyniuk P. M. Nonlinear evolutionary problem of filtration consolidation with the non-classical conjugation condition. Journal of Optimization, Differential Equations and their Applications.
**30**(1), 71–87 (2022). - Kutya T. V., Martynyuk P. N. Mathematical Simulation of Humidification of Earth on a Slope and Calculation of Its Safety Factor. Journal of Engineering Physics and Thermophysics.
**91**, 1189–1198 (2018). - Zhang Q., Zhou Q., Ye F., Yan J., Liu N., Lou Y. Excess Pore Water Pressure and Ground Consolidation Settlement Caused by Grouting of Shield Tunnelling. Mathematical Problems in Engineering.
**2022**, 1854234 (2022). - Ivanchuk N., Martynyuk P., Tsvetkova T., Michuta O. Mathematical modeling and computer simulation of the filtration processes in earth dams. Eastern-European Journal of Enterprise Technologies.
**2**(6), 63–69 (2017). - Gerus V., Martynyuk P., Michuta O. General kinematic boundary conditionin the theory of soil filtration consolidation. Physico-mathematical modeling and informational technologies.
**22**, 23–31 (2015). - Herus V. A., Ivanchuk N. V., Martyniuk P. M. A System Approach to Mathematical and Computer Modeling of Geomigration Processes Using Freefem++ and Parallelization of Computations. Cybernetics and Systems Analysis.
**54**, 284–294 (2018). - Francisca F. M., Glatstein D. A. Long term hydraulic conductivity of compacted soils permeated with landfill leachate. Applied Clay Science.
**49**(3), 187–193 (2010). - Bomba A., Klymiuk Yu., Prysiazhniuk I., Prysiazhniuk O., Safonyk A. Mathematical modeling of wastewater treatment from multicomponent pollution by using microporous particles. AIP Conference Proceedings.
**1773**(1), 040003 (2016). - Sergienko I. V., Deineka V. S. Optimal Control of Distributed Systems with Conjugation Conditions. Springer-Verlag (2005).
- Sergienko I. V., Skopetskiy V. V., Deineka V. S. Mathematical modeling and research of processes in inhomogeneous environments. Naukova Dumka (1991).