A one‐dimensional model for water transport and ice lensing in incompressible saturated and solute‐free soil specimens is proposed for the simulation of small‐scale frost heave tests in the laboratory. The model considers (1) open‐system freezing in which the variables T and Pw are independent, (2) an ice lens that continues to grow as long as enough energy is available in the frozen fringe to produce the work required for mass transfer to the ice lens, and (3) a new ice lens that forms when the vertical strain in the frozen soil reaches the instantaneous tensile failure strain. The proposed frost heave model is amenable to computer simulation procedures which provide predictions of rate of frost heave and rate of pore freezing front penetration as functions of applied load, thermal and water flow regimes, and soil properties. Position, time of initiation, and ultimate thickness of individual ice lenses emerge also as a part of the solution. A quantitative comparison of observed and simulated responses for various boundary conditions is shown for a reference soil known as Devon silt. The model was found to exhibit many of the characteristics observed in frost heave tests on Devon silt and predicted the effects of overburden pressure on frost heave rate.

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Taking into account isotope (13)C value a mathematical model was developed to describe the dynamics of methanogenic population during mesophilic anaerobic digestion of putrescible solid waste and waste imitating Chinese municipal solid waste. Three groups of methanogens were considered in the model including unified hydrogenotrophic methanogens and two aceticlastic methanogens Methanosaeta sp. and Methanosarcina sp. It was assumed that Methanosaeta sp. and Methanosarcina sp. are inhibited by high volatile fatty acids concentration. The total organic and inorganic carbon concentrations, methane production, methane and carbon dioxide partial pressures as well as the isotope (13)C incorporation in PSW and CMSW were used for the model calibration and validation. The model showed that in spite of the high initial biomass concentration of Methanosaeta sp. Methanosarcina sp. became the dominant aceticlastic methanogens in the system. This prediction was confirmed by FISH. It is concluded that Methanosarcina sp. forming multicellular aggregates may resist to inhibition by volatile fatty acids (VFAs) because a slow diffusion rate of the acids limits the VFA concentrations inside the Methanosarcina sp. aggregates.

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