Line Element Method For Three-dimensional Steady And Unsteady Seepage Analysis Of Geotechnical Media

Three-dimensional seepage with free surface is closely related to the safety of many projects,such as slope permeability stability,tailings dam break,tunnel water gushing and oil and gas exploitation.Because the shape of the free surface and the location of the overflow point are unknown in advance,the nonlinearity of the seeping problem with free surface and the difficulty of solving it increase.The current numerical analysis methods for the free surface seepage problem are mainly based on the assumption of continuum by averaging the pore flow in the control body over the entire region containing solid particles.In fact,from the physical process of seepage,water can only flow along pores.the traditional continuous media cannot accurately describe the local seepage behavior of the pores in geotechnical media.Taking geotechnical media as the research object,the linear element method for three-dimensional seepage analysis of geotechnical media is proposed,and the three-dimensional steady and unsteady seepage analysis with free surface is carried out,as well as the influence of reservoir water level change on the stability of dam abutment slope is studied.The main research contents are as follows:（1）The line element method for three-dimensional steady seepage analysis of geotechnical media is proposed.Based on Representative Elementary Volume（REV）,the pore space structure was generalized into a three-dimensional orthogonal network of line elements.According to the principle of flow equivalence,the equivalent seepage velocity,equivalent permeability coefficient and boundary conditions of line elements were deduced.In order to avoid the instability and grid dependence of numerical solution,continuous Heaviside function is used to extend Darcy’s law applicable only to saturated wet zone to the whole seepage zone including dry zone.A line element method for three-dimensional steady seepage with free surface is established and a finite element numerical solution format is given.A program for solving three-dimensional steady seepage problem with free surface is written.The steady seepage analysis of homogeneous rectangular dam,homogeneous right-angle trapezoidal dam and homogeneous isosceles trapezoidal dam with pad drainage is carried out.The applicability and reliability of the line element method are demonstrated by comparing with the numerical simulation results and experimental results of other researchers.The free surface distribution of the homogeneous rectangular dam and the homogeneous rectangular trapezoidal dam under different mesh sizes and penalty parameters is analyzed.It is revealed that the line element method has a low dependence on the mesh size and penalty parameters,but too large mesh size and penalty parameters lead to changes in the free surface distribution of overflow points and overflow surfaces.Through the numerical simulation of the steady seepage of the left bank abutment slope of Kajiwa Hydropower station and the comparative analysis of the calculation results of the continuum model,the results show that the line element method can reflect the seepage field characteristics of the left bank abutment slope of Kajiwa Hydropower station well,which indicates that the line element method has strong applicability and high computational efficiency in dealing with the three-dimensional complex engineering seepage problem.（2）Further extend the line element method of three-dimensional steady seepage analysis to the problem of unsteady seepage,and establish the line element method of three-dimensional unsteady seepage analysis of geotechnical media.Different from steady seepage,the free surface position morphology of unsteady seepage is not fixed,and the singularity of overflow point still exists,which greatly enhances the difficulty of numerical solution.In order to simplify the calculation process of unsteady seepage problem and improve the calculation efficiency,based on the principle of flow equivalence and the local coordinate system,the one-dimensional equivalent forms of seepage velocity,continuity equation and boundary conditions are derived,and the flow recharge conditions when the free surface drops are given,the equivalent feed rate of line element method is derived.A finite element numerical solution scheme of unsteady seepage line element method is constructed by minimizing the functional of continuity equation,and a calculation program for unsteady three-dimensional seepage problem with free surface is written.By numerical analysis of unsteady seepage flow in homogeneous aquifer,trapezoidal dam,drainage sand trough and well unsteady flow model,the correctness and effectiveness of line element method are verified.The effects of different mesh size and time step size on the position morphology and computational efficiency of the free surface are analyzed.It is shown that the accuracy of the line element method is less sensitive to the mesh size and time step.The variation rule of free surface of unsteady flow model under anisotropic and anisotropic conditions is analyzed.It is shown that anisotropy is sensitive to the shape and position of free surface.（3）Based on the three-dimensional seepage and three-dimensional limit equilibrium analysis of geotechnical media,the influence of reservoir water level change on the stability of the slope is analyzed.According to the engineering geological conditions of the slope of the left bank shoulder of Kajiwa hydropower station,a representative landslide body is selected,a three-dimensional geological structure model of the slope is established,the derivation process of the three-dimensional Spencer method is given,and the analysis and calculation process of SLOPE^3D software is introduced;based on the line element method,the change law of the internal free surface of the slope of the left bank shoulder of Kajiwa hydropower station under the condition of reservoir water level change is calculated,combined with SLOPE^3D software calculates the corresponding safety coefficient of the slope under the effect of seepage,and analyzes the influence of the change of reservoir level on the safety coefficient of the slope.The results show that:the change of reservoir level has a greater influence on the seepage field at the shoulder of the dam,but less on the internal seepage field of the slope;when the reservoir level rises,the free surface rises,and the safety coefficient of slope stability decreases,and the faster the reservoir level rises,the faster the safety coefficient of slope decreases;on the contrary,when the reservoir level decreases,the free surface decreases,and the safety coefficient of slope stability increases gradually,and the faster the reservoir level decreases,the faster the safety coefficient of slope increases.The faster the reservoir level decreases,the faster the safety factor of the slope increases.