Verification of a macro-element method in the numerical simulation of the pore water pressure dissipation method - A case study on a liquefaction countermeasure with vertical drains under an embankment

In the simulation of the vertical drain method using a soil-water coupled finite element analysis, a macro-element method has often been used as an approximate method to introduce the water absorption functions of drains into individual elements. In order to extend the function of this method, the authors modified the formula of the flow coefficient from soil to drains and introduced the discharge function of vertical drains to the method by treating the water pressure in the drains as an unknown and adding a continuity equation for the drains to the governing equations. The first attempt made it possible to divide a finite element mesh independently of the drain arrangement and the drain spacing, and the second attempt enabled the well resistance to be automatically generated by a series of calculations depending on the given conditions. Furthermore, although the macro-element method has been applied to quasi-static problems in most cases, the authors applied the expanded one to dynamic problems by equipping it with the soil-water coupled finite deformation analysis code GEOASIA with the inertial term. In this paper, in order to verify the new macro-element method in a dynamic problem, the results of a 2D approximate model using the new macro-element method were compared with those of a 3D exact model where vertical drains were exactly represented by finely dividing the finite element mesh in the case of a sand ground improved by the pore water pressure dissipation method under the embankment. The findings of this study are as follows: (1) 2D mesh-based analyses under plane strain conditions, using the new macro-element method, can accurately approximate 3D mesh-based analyses with a fine mesh in dynamic problems in terms of changes in the excess pore water pressure and ground deformation; (2) the new macro-element method can adequately evaluate the influence of drain spacing on a countermeasure for liquefaction in the quantitative sense, while using a single mesh; and (3) the new macro-element method improves the calculation efficiency in the simulation of the pore water pressure dissipation method by laborsaving in mesh-dividing and dramatically reducing the calculation time.