Analytical Analysis On One-dimensional Finite Strain Nonlinear Consolidation Of Saturated Soft Clay

The conventional infinitesimal strain consolidated theory may meet the demand of the general engineering when the degree of the applied load is not very high and the geological conditions of siol layers are rather good.While the degree of the applied load is rather high and the geological conditions are not good enough,its direct application would lead to a rather bigger error, but if we consider finite strain consolidated character of the foundation of the soft soils and apply finite strain consolidated theory to analyze it, its effect would be in more accordance with actuality. So it is very necessary to study the finite strain consolidated theory of the soft clay soils deeply.On the basis of rather more general assumptions than those usually adopted by Terzaghi, Rendulic , Biot, etc,Gibson et al derived a differential equation governing the progress of one-dimensional finite strain consolidated, the equation can be shown as a nonlinear equation.Gibson and many researcher later had been done on the nonlinear equation during the past decades with the assumptions that parameter g ( e ) andλ( e) are constant. According to the above mentioned, the nonlinear equation would be transformed into a linear one and a mathematical solution can be obtained. But so far the analytical solution of this theory has not almost been studied.So we mean to study the analytical solution of the theory in this article.Many researches show that it is difficult to obtain an analytical solution, even an approximate one for this nonlinear equation of finite strain consolidated if without any further presumption on it.So pointing at the above mentioned, two assumptions about the compressibility and permeability of saturated soft clay are taken in this article.And then, by the two assumptions given in this article, the equation of governing the progress of finite strain consolidation can be transformed into a rather simple one.By using the approach of transformation of Hopf-Cole, the equation can be transformed into a linear parabolic form and the exact analytical solution on the relatively simpler well-posed condition is obtained.In the end, the obtained theoretical analytical solutions are used to calculate the settlement and time of consolidation of a practical engineering, then compared with the results in Cargill's method and results in Terzaghi's theory. It is shown that the model applied in this article is reasonable. Meanwhile some problems appeared in calculation are analyzed.