Permeability Characteristics Of Unsaturated Loess Based On Fractal Theory

Natural geological disasters in loess areas are frequent,such as collapses,landslides,debris flows,etc.,and the occurrence of these problems is related to the infiltration of water in unsaturated loess.The soil-water characteristic curve and unsaturated permeability coefficient reflect the water-holding characteristics and permeability characteristics of loess in the process of unsaturated infiltration,respectively,and accurate acquisition of soil-water characteristic curve and unsaturated permeability coefficient is the basis and key point to solve the disaster problem and engineering construction in loess area.The traditional empirical formula for obtaining soil-water characteristic curves and unsaturated permeability coefficients contains empirical parameters without clear physical significance,and the calculation is cumbersome,and there is a certain error between the results and the actual situation,which has a certain impact on the construction and management of loess areas.Fractal theory is an effective means to quantitatively describe the complex structure of soil and predict the hydraulic properties of soil.Therefore,taking the soil-water characteristic curve and unsaturated permeability coefficient of unsaturated loess as the research object,based on fractal theory,combined with field survey sampling,related experiments and numerical simulation,this paper analyzed the granular fractal characteristics of loess（L₁,L₆and S₁）in three different periods of the south bank of Jingyang,established the soil-water characteristic curve of unsaturated loess and the fractal model of unsaturated permeability coefficient,and obtained hydraulic characteristic parameters.At the same time,the specific physical significance of the parameters was given,and a simple method for obtaining the relevant parameters was proposed,on this basis,the water infiltration law of unsaturated loess under different rainfall conditions was summarized.The main research results were as follows:（1）The particle distribution curves of L₁,L₆and S₁in the south bank of Jingyang were determined by laser particle size analyzer,the fractal dimension of particle mass was calculated,and the fractal characteristics were analyzed.According to the results of the particle mass fractal model,the three soil samples did not have fractal characteristics in the range of particle size less than 1μm,and the fractal dimension of particle mass calculated in the range of 1～50μm can best characterize the structural characteristics of loess and ancient soil.The fractal dimension D of the particle mass of the three soil samples was sorted as:S₁>L₁>L₆,the fractal dimension of soil particles could be used as a quantitative index to judge the particle size components and texture status of the soil,the larger the value of the fractal dimension,indicating that the average particle size of the soil is smaller,the more clay content,and the finer the texture.（2）The soil-water characteristic curves of L₁,L₆and S₁were determined by contact filter paper method,and the applicability of classical models and fractal models and the relationship between the two models were discussed.The classical model fitting results show that the Brooks Corey model is used to fit the soil-water characteristic curves of the three soil samples well.Based on the fractal model of soil-water characteristic curve based on particle mass distribution,the soil-water characteristic curve fitting degree of these three soil samples was high,and the R²was above 0.90.The relative error between the fitted pore fractal dimension D’and the empirical constant n in the Brooks Corey model and the fractal dimension D of soil particle mass is less than 10%,respectively,and the particle fractal dimension D can be used instead of the difficult-to-obtain pore fractal dimension and the empirical constant without physical significance.（3）Relying on the fractal dimension D of particles and the air-entry value?_aev,the fractal model of the relative permeability coefficient of L₁original loess was established,and the saturated and unsaturated permeability coefficients were determined by the permeability test of the constant water head and the principle based on the combination of filter paper method and transient profile method,which verified the reliability of the parameters in the model.By comparing the fractal model function curve with the experimental measured data,it was found that the established relative permeability coefficient fractal model is close to the measured data,and it is believed that the fractal dimension D of the particles and air-entry value?_aevin the model could accurately describe the permeation characteristics of unsaturated loess,which could be further applied.（4）The fractal model of unsaturated loess hydraulic features was introduced into the HYDRUS-1D water flow model,and the model parameters were verified by using the results of rainfall infiltration monitoring in the previous field.The water transport law of unsaturated loess under different rainfall conditions was revealed.The numerical simulation results of HYDRUS-1D showed that the infiltration of water in the soil is divided into three stages:stable and unchanged section,rapid increase of volume moisture content and slow change of volume moisture content.The water infiltration law of loess is different under different rainfall intensities,and the greater the rainfall intensity,the faster the water infiltration rate.Under heavy rainfall and rainstorm conditions,the water only penetrated to 40 cm at 48 h,but did not penetrate into deeper soil layers.Under the condition of heavy rainstorm,the water infiltrated into the soil within 1 m,and the moisture content of the soil within 60 cm reached a stable state,but it was not saturated.The numerical simulation results provide a basic basis for soil stability under rainfall conditions,which is of great significance to the engineering construction of loess areas.