This article deals with several hysteresis effects occurring in soils and other porous media. Soils consist of solid particles which are of different size, shape and material behavior depending on the soil type. The pore space is filled with one pore fluid for saturated porous media, with two or more immiscible fluids for partially or unsaturated media. Most of the hysteresis phenomena described can be traced back to the behavior of the pore fluids, e.g., they have to do with different capillary pressures for different degrees of saturation. Hysteresis describes that a quantity or process is not single-valued, that in dependence on the prehistory for the same input value two or more possible output values may occur. The aim of the paper is to show various examples for which hysteresis effects occur and to discuss the reasons – either theoretically or experimentally. Triggered by an actual incident, highlighted in the introduction, in a first paragraph stage/discharge hysteresis of rivers is explained. The most prominent type of hysteresis, hydraulic hysteresis, is treated in the next section. Engineering and mathematical approaches are discussed and results of own laboratory experiments are shown. Further pairs of processes leading to non-unique behavior are adsorption/desorption processes or freezing/thawing processes. But not only the behavior and properties of the pore fluids lead to hysteretic effects. Also the constitutive relations of dry soils exhibit hysteresis. Generally, soils behave differently if first loaded, unloaded and reloaded. It is shown in a further paragraph that the stress-strain curves are hysteretic. The aim of the paper is to show that in porous media where the solid and fluid components interact, accordingly, a variety of hysteresis effects appear and to highlight the different phenomena, show the variety of hysteresis curves and indicate description methods.
Citation: Bettina Detmann. On several types of hysteresis phenomena appearing in porous media[J]. Mathematics in Engineering, 2025, 7(3): 384-405. doi: 10.3934/mine.2025016
This article deals with several hysteresis effects occurring in soils and other porous media. Soils consist of solid particles which are of different size, shape and material behavior depending on the soil type. The pore space is filled with one pore fluid for saturated porous media, with two or more immiscible fluids for partially or unsaturated media. Most of the hysteresis phenomena described can be traced back to the behavior of the pore fluids, e.g., they have to do with different capillary pressures for different degrees of saturation. Hysteresis describes that a quantity or process is not single-valued, that in dependence on the prehistory for the same input value two or more possible output values may occur. The aim of the paper is to show various examples for which hysteresis effects occur and to discuss the reasons – either theoretically or experimentally. Triggered by an actual incident, highlighted in the introduction, in a first paragraph stage/discharge hysteresis of rivers is explained. The most prominent type of hysteresis, hydraulic hysteresis, is treated in the next section. Engineering and mathematical approaches are discussed and results of own laboratory experiments are shown. Further pairs of processes leading to non-unique behavior are adsorption/desorption processes or freezing/thawing processes. But not only the behavior and properties of the pore fluids lead to hysteretic effects. Also the constitutive relations of dry soils exhibit hysteresis. Generally, soils behave differently if first loaded, unloaded and reloaded. It is shown in a further paragraph that the stress-strain curves are hysteretic. The aim of the paper is to show that in porous media where the solid and fluid components interact, accordingly, a variety of hysteresis effects appear and to highlight the different phenomena, show the variety of hysteresis curves and indicate description methods.
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Bettina Detmann. On several types of hysteresis phenomena appearing in porous media[J]. Mathematics in Engineering, 2025, 7(3): 384-405. doi: 10.3934/mine.2025016
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