Solution of Terzaghi one-dimensional consolidation equation with general boundary conditions

Boundary conditions for the classical solution of the Terzaghi one-dimensional consolidation equation conflict with the equation＇s initial condition. As such, the classical initial-boundary value problem for the Terzaghi one-dimensional consolidation equation is not well-posed. Moreover, the classical boundary conditions of the equation can only be applied to problems with either perfectly pervious or perfectly impervious boundaries. General boundary conditions are proposed to overcome these shortcomings and thus transfer the solution of the Terzaghi one-dimensional consolidation equation to a well-posed initial boundary value problem. The solution for proposed general boundary conditions is validated by comparing it to the classical solution. The actual field drainage conditions can be simulated by adjusting the values of parameters b and c given in the proposed general botmdary conditions. For relatively high coefficient of consolidation, just one term in series expansions is enough to obtain results with acceptable accuracy.

Consolidation analysis of composite foundation with partially penetrated cement fly-ash gravel(CFG) piles under changing permeable boundary conditions

Based on the double-layered foundation theory, the composite ground with partially penetrated cement fly-ash gravel(CFG) piles was regarded as a double-layered foundation including the surface reinforced area and the underlying untreated stratum. Due to the changing permeability property of CFG piles, the whole consolidation process of the composite ground with CFG piles was divided into two stages, i.e., the early stage(permeable CFG pile bodies) and the later stage(impermeable pile bodies). Then, the consolidation equation of the composite foundation with CFG piles was established by using the Terzaghi one-dimensional consolidation theory. Consequently, the unified formula to calculate the excess pore water pressure was derived with the specific solutions for the consolidation degree of composite ground, reinforced area and underlying stratum under instant load obtained respectively. Finally, combined with a numerical example, influencing rules by main factors(including the replacement rate m, the treatment depth h1, the permeability coefficient Ks1, Kv2 and compression modulus Es1, Es2 of reinforced area and underlying stratum) on the consolidation property of composite ground with CFG piles were discussed in detail. The result shows that the consolidation velocity of underlying stratum is slower than that of the reinforced area. However, the consolidation velocity of underlying stratum is slow at first then fast as a result of the transferring of effective stress to the underlying stratum during the dissipating process of excess pore water pressure.

CONSOLIDATION THEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅱ)

The present paper uses the mathematics model for consolidation of unsaturated soil developed in ref.[I]to solve boundary value problems.The analytical solutions for one-dimensional consolidation problem are gained by making use of Laplace transform and finite Fourier transform.The displacement and the pore water pressure as well as the pore gas pressure are found from governing equations simultaneously.The theoretical formulae of coefficient and degree of consolidation are also given in the paper.With the help of the method of Galerkin Weighted Residuals,the finite element equations for two-dimensional consolidation problem are derived.A FORTRAN program named CSU8 using 8-node isoparameter element is designed.A plane strain consolidation problem is solved using the program,and some distinguishing features on consolidation of unsaturated soil and certain peculiarities on numerical analysis are revealed.These achievements make it convenient to apply the theory proposed by the author in engineering practice.

Law of nonlinear flow in saturated clays and radial consolidation

It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A math- ematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Re- sults show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.