Studies On The Analytical Theory Of One Dimensional Large Strain Consolidation Problem

The development of finite strain consolidation theories based on continua mechanics and mixture theory is detailed and the differences and consistency between these theories are remarked on. With the method of the Lie group transformation,the symmetry of the equation governing one dimensional finite strain consolidation is discussed and,from the point of the symmetry,the feasibility to obtain the analytical solution of these nonlinear partial differential equations is discussed. Where-after exact or approximate analytical solutions focused on different consolidation problems are obtained,these including:Under some assumptions of relations of the void ratio with coefficient of permeability and effective stress,the method of Lie group transformation is applied to solve the non-linear partial differential equation of large strain consolidation of homogenous saturated clay soil in semi-infinite domain with the consideration of the material and geometrical nonlinearity during consolidation procession. The implicit exact solution without considering the effect of self-weight of soil is obtained. The comparison depended on the results of the nonlinear theory and conventional theory is presented. The relationship between the non-linear and the linear theories is discussed and a more reasonable method to determine the consolidation coefficient in conventional theory is brought forward.The consistency between the material and geometrical descriptions of one dimensional nonlinear large strain consolidation models with certain initial and boundary conditions is discussed. The properties of different kinds of transformed boundaries are evaluated. The characteristics of different boundary conditions are evaluated. By applying the approach of the transformation of Lie group,the exact analytical solutions of the non-linear consolidation equation is obtained under different initial and boundary conditions. Based on this solution,the differences between that of large and infinite strain consolidation theories are analyzed. The result of a case studying shows that the settlement calculated by large strain consolidation theory is large than that by infinite strain theory during the consolidation procession,but the final settlements calculated by both theories are same.More general assumptions than that in the classical consolidation theory is adopted and the exact analytical solution of nonlinear finite strain self-weight consolidation based on this assumption is obtained. By applying same experiment data,the comparison of the solutions of linear and nonlinear finite strain theory,as well as the numerical solution from finite element method is presented. The result of the comparison shows that the analytical solution obtained here takes on better agreement with practical cases than that of linear one,and the result also shows that,comparing to the solution from nonlinear theory,the evaluation of the settlement and the consolidation degree from linear theory is small.As a primary part of self-weight consolidation,a mathematical model for sedimentation in the steady water,with the volume fraction of the soils as its depended variable,is established. The model shows that the progress of the sediment of the soils is similar to the propagation of the shock wave. Under certain initial conditions,the analytical solution is obtained by applied Lagrangian series method. The rationality and the validity of the solution achieved are shown by a case study of coal mine tailing slurry.A finite strain nonlinear model to simulate the consolidation procession with accumulation on top boundary is established. Owing to the symmetry of the model,a similar variable is constructed and based on this similar variable,and an approximate analytical solution of the model is obtained by using perturbation method. After applying same experiment data,the comparison between the solutions obtained here and the solutions appeared in classical linear theory is presented,and the shortcoming in classical linear theory is shown.The consistency amo...