Abstract:Considering the well resistance and the smear effects,the numerical modeling and the solution method for multi-layered clays consolidation by partially penetrated vertical drains under time-dependent loading are presented. Assuming a virtual drain penetrating the soft strata at the bottom of the actual drain,the partially penetrated vertical drain is transformed into a fully penetrated vertical drain,thus the boundary conditions for consolidation equations and the numerical process are simplified. The excess pore water pressure of each stratum is interpolated and approximated by Lagrange interpolation polynomials;and the algebraic equations of excess pore water pressure at boundary nodal points are obtained with inner nodal points. Thus the consolidation equations of the section with vertical drains are transformed into simple differential equations describing the values of excess pore water pressure in the nodes,and linear algebraic simultaneous equations of vertical drains consolidation in the nodes are obtained simultaneously. For the four-layer soils,the calculating formulas are presented in detail. If the number of soil layers is added,the boundary nodal coefficient formulas are changed only. The presented numerical results are compared with those using the relevant approximate methods;and an example of roadbed composed of four soft soil layers under preloading is analyzed. It is shown that there are no much differences between the one-dimensional model and the three-dimensional model adopted in the underlying undrained zone.