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Abstract: The paper describes prediction of thermal conductivity in terrestrial soil media. The model operates statistically by probability of occurrence for contacts between particular fractional compounds. It combines physical properties, specific to particular compounds, into one apparent conductance specific to the mixture. The concept of substituting grain compounds by hypothetical spheres is an essential tool to control porosity by the number of spheres, their radii and probability of contacts between them. The spheres are equal in radii. The spheres substitute compounds, regardless of the phase state. Control of particular phase states is possible by means of specific properties assigned to the spheres, at the input to the model. Performance of the model is successfully proved for many diverse terrestrial soil media in a wide range of bulk density, composition, water and water vapour content. Only the compounds of sand decline from the expected values and require introducing a correction to the thermal conductivity of sand grains. One possible explanation is that the thermal conductivity of sand is uncertain. Nevertheless, the model is useful and worth extending beyond terrestrial purposes. [Copyright &y& Elsevier]

Soil compaction influences crop growth, movement of water and chemicals in numerous ways. Mathematical modelling contributes to better understanding of the complex and variable effects. This paper reviews models for simulating topsoil and subsoil compaction effects. The need for including both topsoil and subsoil compaction results from still increasing compactive effect of vehicular pressure which penetrates more and more into the subsoil and which is very persistent. The models vary widely in their conceptual approach, degree of complexity, input parameters and output presentation. Mechanistic and deterministic models were most frequently used. To characterise soil compactness, the models use bulk density and/or penetration resistance and water content data. In most models root growth is predicted as a function of mechanical impedance and water status of soil and crop yield—from interactions of soil water and plant transpiration and assimilation. Models for predicting movement of water and chemicals are based on the Darcy/Richards one-dimensional flow equation. The effect of soil compaction is considered by changing hydraulic conductivity, water retention and root growth. The models available allow assessment of the effects of topsoil and subsoil compaction on crop yield, vertical root distribution, chemical movement and soil erosion. The performance of some models was improved by considering macro-porosity and strength discontinuity (spatial and temporal variability of material parameters). Scarcity of experimental data on the heterogeneity is a constraint in modelling the effects of soil compaction. Suitability of most models was determined under given site conditions. Few of the models (i.e. SIBIL and SIMWASER) were found to be satisfactory in modelling the effect of soil compaction on soil water dynamics and crop growth under different climate and soil conditions. [Copyright &y& Elsevier]