###### Abstract  
To optimize the design of stone columns composite foundation for liquefiable ground improvement in the Tibar Bay Port Project, a 3D Finite Element (FE) analysis is implemented on the earthquake response and liquefaction mitigation effect. Nine improvement schemes are designed with the orthogonal design method. Taking peak ground acceleration and peak excess pore pressure ratio as the target indicators, the influences of four factors, including diameter, replacement ratio, stiffness, permeability ratio, of stone columns are analyzed by means of range analysis, and subsequently, the optimal ground improvement design is obtained. The analysis results indicate that the responses of ground acceleration and excess pore pressure ratio are relatively sensitive to stone columns' permeability ratio and a little sensitive to the replacement ratio. The stiffness and diameter ranging in the prescribed boundary only have negligible effect. The mitigation effect of drainage is rather significant when the ratio of the stone columns' permeability to the soils' permeability is greater than 100.  
liquidefiable ground; stone columns; orthogonal design method; dynamic response analysis; opensees +
Footnote †: journal: Medical  
has not been proposed. As made up of granular material, the granular columns' mechanical behaviors and deformation patterns are closely related to the mechanical properties and deformation of surrounding soils, which adds complexity to investigating the earthquake response characteristics of the composite foundation and generalizing an applicable design approach. Therefore, pertinent studies are still needed for granular columns in particular engineering sites. The dynamic numerical analysis is a fundamental means to study the earthquake response of granular columns composite foundation in liquefiable soils, among which the FE analysis based on [PERSON]'s dynamic consolidation equation can fully couple the pore pressure with the dynamic response of the soil skeleton and becomes one of the most extensively used approaches [14]. In order to assess the effectiveness and mitigation of stone columns, three-dimensional FE simulations were implemented on OpenSees in various studies [15; 16; 17; 18; 19] with the same computational formulation. These studies assumed the saturated soils to be solid-fluid material following the u-p formulation which is developed based on [PERSON]'s theory by [PERSON] [20] and [PERSON] et al. [21]. The u denotes displacement of the soil skeleton and p denotes pore pressure. The multiple yield surface elastoplastic constitutive model, PDMY (PressureDependMultiYield), was adopted in these studies to simulate the materials of both surrounding soils and granular columns. The seismic responses of the granular column composite foundation were simulated. Furthermore, the liquefaction mitigation effects were analyzed such as the shear reinforcement, and the lateral displacements restraining. [PERSON] et al. [22] applied the same numerical method to simulate the centrifuge test of the saturated silty site improved with granular columns and analyzed the dynamic characteristics such as ground acceleration and pore pressure. Hereby, the results indicated that the numerical simulation was in good agreement with the experimental measurement. There are also FE simulations based on u-p formulations with other constitutive models, such as the hypoplastic model [23] and critical state model based on generalized plasticity theory [24], which are conducted to evaluate the performance of granular columns in liquefaction mitigation. Additionally, [PERSON] et al. [25] used FLAC3D for dynamic response analysis, applied the elastoplastic constitutive model which is able to predict the large post liquefaction deformation and equivalent nonlinear model to simulate materials of sand and granular columns, respectively, and evaluated the liquefaction mitigation effect in terms of shear reinforcement and drainage of the granular columns.