Study On Homogenization Theory And Its Application To Sand-drained Ground

The homogenization theory is a valid analysis method which is introduced to express the heterogeneity (materials and fields etc.). The underlying interpretation is that homogenization theory first can be attempted to develop the analysis of the Geotechnical Engineering problems. Particularly speaking, homogenization theory based on the fundamental problem-consolidation in the Geotechnical Engineering, which has following advantages and conclusions compared with other methods:1. On the basis of equilibrium equation, geometrical equation, linear constitutive equation, effective stress analysis and seepage equation, the consolidation equation is deduced of the inhomogeneous, isotropic and linear elastic soil, and solved for a typical one-dimensional consolidation problem. It is shown that the result obtained by using the equation has a good agreement with those of other methods, such as T.T (Total stress analysis combined with Terzaghi's consolidation theory) and Biot.2. When ignoring the micro-variable's distributions, we assume that material is composed of linearly elastic inclusion and matrix. The study area is made up of 1mm×1mm square base cell with the same inclusion ratio (η%). Some important conclusions as to the influence of inclusion ratio on micro-structure equivalent modulus can be obtained: equivalent modulus is a linear trend with inclusion ratio for the given inclusion. Whenη%<30% or >90%, any model can be applied for the material whose micro-structure is unknown; and the heterogeneity can be taken as the isotropic homogeneity with the same modulus of matrix (inclusion) whenη%<5% (>95%).3. In this paper, the FEM-equations are obtained for lateral equivalent hydraulic conductivity (Kh) of sand-drained ground based on the homogenization theory.4. Upon the axial symmetric analysis of sand-drained ground, the influence of sand drain to all base vertical permeability increasing is equal to the hydraulic conductivity of Terzaghi's one-dimensional consolidation equation by the numerical calculation, and then vertical equivalent hydraulic conductivity (Kv) of sand-drained ground is obtained.All above, a new method is described for consolidation analysis of sand-drained ground, that is, Kh and Kv are used to transform the consolidation problem of sand-drained ground to non-sand-drained ground, then FEM analysis of 3-D Biot's consolidation is obtained. At last, the method introduced has been applied to a project by FEM calculation, which demonstrates its effective simulation and validation on inhomogenizatical settlement, lateral deformation, radial seepage in the reinforcement ground and the diffuse of pressure in the soil of sand-drained ground.