Modification of the filtration consolidation equation and kinematic boundary condition into the case of biodegradation processes

This work considers the modification of the filtration consolidation equation to describe the settlement processes of municipal solid waste (MSW) landfills, taking into account the influence of biodegradation processes. The mathematical model incorporates the thermal effect resulting from biodegradation processes and introduces boundary conditions to describe the interaction of heat and fluid pressure. The corresponding mathematical model is described by the Stefan boundary value problem for a system of differential equations of biodegradation and two quasilinear parabolic equations. One of the equations describes the change in thermal state in a porous medium, while the other describes the change in excess pore pressure in the pore fluid. This approach allows for avoiding the determination of the stress-strain state and modeling the microbiological dynamics. The finite element method was used to find the solutions to the corresponding boundary value problem. The obtained results assess the change in the dynamics of the settlement of MSW landfills considering biodegradation and non-isothermal conditions