Rational Approximation for Uni-Dimensional Consolidation Differential Equation of Saturated Soil

As the basic equation of soil mechanics, the Terzaghi consolidation equation of soil can be expand into Taylor polynomial model which meets the precision demands on engineering. Thus the equation is suitable to solve in nonlinearity for using the method of Pade rational approximation. Based on variables discretization and matrixation, the solution of uni-dimensional consolidation equation of saturated soil is transformed to the process of rational approximation on matrix exponential function. The approximation procedure indicates that the rational approximation is effective on functions expression for those functions are characterized on their expression prone to compute. Moreover, the induction process shows that the consolidation equation by variables discretization and step approximation is suitable for programming because of good approximation and the stability on numerical calculation. These are ready for the theoretical basis in the numerical simulation of rational approximation on multi-dimension consolidation also.