Research On Hydraulic Characteristics And Hysteresis Model Of Unsaturated Soil Based On Fractal Theory

In geotechnical engineering,the description of hydraulic characteristics of unsaturated soils is mainly based on two constitutive relationships: soil water retention curve and relative permeability curve.In most of the analytical models of hydraulic characteristics of unsaturated soils,the modeling of soil water characteristic curves and relative permeability curves is usually based on the capillary action of the soil pore scale and the viscous flow of the fluid.However,due to the complexity of the soil pore space and the variability of its hydraulic behavior,there are still huge challenges for the accurate modeling of these two constitutive relations.In this paper,based on the microscopic physical behavior of unsaturated soil under hydraulic load,combined with soil pore structure characteristics,soil agglomeration water holding characteristics and pore fluid transport characteristics,the soil water characteristic curve,relative permeability curve and the corresponding hysteresis effect of unsaturated soil are mainly studied.The main research results are as follows:(1)By analyzing the microstructure and size distribution characteristics of soil pores,six different pore size distribution functions are summarized.Combined with the soil water retention characteristic and Young-Laplace equation,water retention curve equations with different pore size distribution functions are established.The physical fact that the soil water retention curve is controlled by the microscopic pore distribution is revealed.Introducing the fractal theory,a fractal capillary model with a pore-throat structure is established,which can reflect the hysteresis effect of the water retention curve from the physical level.The derived water retention curve model based on fractal theory can intuitively reflect the influence of pore size distribution,pore tortuosity and pore throat size on unsaturated soil water-holding properties.The model is used to predict the experimental data under different hydraulic paths.The results show that the fractal capillary model can predict the soil water retention characteristics and hysteresis effects under dry and wet paths.(2)The hysteresis model of the full-path soil water retention curve based on pore expansion and contraction under different hydraulic paths is established,and the physical laws of pore space structure evolution under different hydraulic loads are revealed.Based on the test results,the model determines the evolution characteristics of soil pores under hydraulic load by analyzing the commonness and difference of soil water retention curves under mechanical load and hydraulic load.Then the hysteresis increment equation of the water holding curve based on pore expansion and contraction is established,and the model is verified by experimental data.The results show that the model in this paper can predict the arbitrary path scanning curve and the main dry and wet curve better.In addition,based on the data analysis,the expansion and contraction laws of the corresponding soil pores can be obtained,thereby quantifying the expansion and contraction behavior of the pore microstructure of the soil under the action of hydraulic loading.(3)Under the assumption of laminar flow,a generalized statistical model of relative permeability of two-phase flow in non-uniform pores is established.The introduction of pore non-uniformity factors expands the Darcy law and BuckinghamDarcy law.Furthermore,by analyzing the characteristics of fluid transport and combining with Hagen-Poiseuille law,the generalized relative permeability model of unsaturated soil in wet and non-wet phases is derived.This model can be derived by embedding the pore size distribution function of any unsaturated soil.In this paper,taking the fractal scale law of pore size distribution as an example,a fractal model and a Monte Carlo model for the relative permeability of two-phase flow in non-uniform pores are established.The test data of different wet-non-wet phase systems(including water-air,water-steam,water-nitrogen,water-oil,oil-gas systems)are used to verify the model.The results show that the established fractal permeability model can better describe the transport characteristics of different fluid systems.In addition,through comparison with the VG-M and BC-M models,it is found that the model of this paper overcomes the shortcomings that the predicted values of the VG-M and BC-M models are generally too large,proving that the model of this paper has obvious advantages.On this basis,based on the non-uniformity of the pores,a hysteresis model of the relative permeability of the wet and non-wet phases is established.The model better reveals the essence of the hysteresis characteristic of fluid transport in non-uniform pores,namely the dependence of the hysteresis effect on independent variables.