Numerical Solution And Analysis Of One-Dimensional And Two-Dimensional Consolidation Equations Under Complex Conditions

Since Terzaghi founded the one-dimensional consolidation theory,many domestic and foreign researchers have devoted themselves to correcting the assumption of it.Consolidation solutions under complex conditions often rely on numerical solutions,of which the finite difference method is an effective way to deal with consolidation of partial differential equations.Because of the complicated programming of differential formats under complex conditions,the high probability of human error,and the difficulty of debugging,the author proposed the Excel difference method.The principle of Excel finite difference method is to use the cells in Excel to replace the nodes in the finite difference method.Combining Excel’s powerful ability to calculate and store data,this paper deals with one-dimensional homogeneous foundations,variable loads,layered soils,changes in soil thickness,semi-permeable boundaries and other complex conditions and two-dimensional homogeneous foundations,and compare the homogeneous foundation deduced by Terzaghi,variable load derived by Shiffman,semi-permeability of layered soil deduced by Xie Kanghe and the two-dimensional homogeneous foundation analytical solution derived by Huang Chuanzhi.It is found that the Excel finite difference method has high accuracy and rapid calculation.After proving the rationality and reliability of Excel finite difference method,this paper studies the following questions:(1)Solve the two-dimensional consolidation difference solution under semi permeable boundary condition.give a two-dimensional consolidation solution under semi-permeable boundary conditions,plot the average consolidation degree curve of any section,and the load center position of super-static vertical distribution curve and the consolidation degree curve of pore pressure,analyze the consolidation characteristics of the two-dimensional semi-permeable boundary,and prove that the boundary conditions and the calculation dimension have a very large influence on the degree of consolidation.(2)Two-dimensional consolidation differential solutions are given for both linear and cyclic loads.The average consolidation degree curves for arbitrary sections of line load are plotted and the center of loading is plotted,too.The vertical distribution curve of the excessive static pore pressure and the overall average consolidation curve of the foundation directly below the load,and the overall mean excess pore pressure and the mean effective stress change curve of the foundation directly below the cyclic load are also obtained.For the consolidation characteristics,it is shown that the overall mean excess pore pressure and the mean effective stress of the foundation directly below the cyclic load are oscillating with a certain curve,and the change of the mean effective stress is not synchronized with the load.(3)Solve the one-dimensional consolidation problem of double-layer foundation with multi-level loading and semi-pervious boundary,and verify that the error of consolidation degree in Gao MuJunJie method and Excel difference method is small,and analyze the load slope of multi-level loading under simple conditions on the effect of excess pore pressure and degree of consolidation was plotted,plot the space-time distribution of the excess pore pressure under multi-stage loading under complex conditions and investigate the effect of loading mode and boundary conditions on the average excess pore pressure and degree of consolidation.(4)The analytical solution of the one-dimensional consolidation equation for single-surface continuous drainage boundary under the action of instantaneous plus dead loads and varying loads is derived and compared with the numerical solutions obtained by Matlab and Excel.It is found that the error of the three methods is very small and the reliability of the numerical method is proved.Sex and accuracy also prove the correctness of the analytical solution.At the same time,the continuous drainage boundary is used to estimate the value of the semipermeable boundary parameter,which is mainly to use Matlab to compile a numerical calculation program to inversely analyze the value of R.