1-D Consolidation Analysis For Saturated Soft Clay Considering Hyperbola Model And Non-darcy Flow

As the development of the highway construction, many embankments were built on soft soil. At the same time, more attention was drawn to the consolidation problem with time as well as depth dependent load. The traditional Terzaghi one dimensional consolidation theory assumes that the soil is linear elastic material and the validity of darcy's law with constant the permeability coefficient. However, the characteristics of clay is complex, especially for soft clay. Its stress—strain relationship and seepage properties are influenced by a plenty of factors. As a result, it is defective to make the assumption as Terzaghi did. Actually, when applying to practical projects, the solution derived by Terzaghi theory is not accurate enough. In order to solve the accuracy problem above, it is important to devote to nonlinear consolidation theory.There are many ways, such as considering nonlinear stress—strain relationship, nonlinear seepage properties, time dependent load, layers, nonlinear boundary conditions and the like, to improve the tranditional Terzaghi consolidation theory. Mainly two kinds of nonlinear soil constitutive modes are used in consolidation problem. One of them is called the nonlinear elastic model(or experiential model), such as, hyperbolic model and e~lg?' model. Another soil constitutive mode is named rheological model which assumes the soil viscoelastic plastic body, for example Maxwell model?Kelvin model?Merchant model and so on. The e~lg?' model is frequently used in analysis of nonlinear consolidation on which experiential mode is based. However, it is the key point to evaluate the preload while how to figure out the precise preload is still on debat. Compared with e~lg?' model, hyperbolic model, which has a more simple and practical expression, can meet the in-situ need when calculating the displacement because the effect of the preload is ignored. The seepage properties of soil is also a factor that essentially affects the process of consolidation. Plenty of research done so far reveals that the e~lgk model, which describes how k changes as the consolidation process develops, is reliable. What is more, after 45 years' observation and research, Hansbo has discovered that the darcy's law is not always accurate, especially for the soft clay. Thus, he has presented a series of new equations to simulate the nonlinear relationship of velocity of flow v and hydraulic gradient i, which is called non-darcy flow. Experiments carried out by hansbo showed much evidence which supported the new equations.As a result, based on the research before, in this paper,assuming the gravity stress of soil varies with depty,assuming the effective stress caused by loading changes with depty as well as time,using hyperbolic model to simulate the stress—strain relationship, and considering the validity of the non-darcy flow, the governing equation of the improved nonlinear hyperbolic model of one dimensional consolidation theory can be derived.Because the governing equation derived is too difficult to give a analytical solution, finite difference method is introduced. This paper transform the complex governing equation into finite difference scheme by using Crack-Nicholson difference method. For the weak nonlinear difference scheme, a explicit difference scheme can be given by linearization. For the strong nonlinear difference scheme, iteration method was used to solve the problem. So, the numerical solution of the governing equations are derived. Then, the numerical solution scheme was divided to two parts which owned diverse density of the scheme net so that efficiency were improved as well as time was saved.At last, compared with the analytical solution derived before and a experiment observation, the theory presented in this paper was proved validate.