Research Paper A simplified axisymmetric model for column supported embankment systems Lin-Shuang Zhao a , Wan-Huan Zhou a,b,⇑ , Ka-Veng Yuen a a Department of Civil and Environmental Engineering, Faculty of Science and Technology, University of Macau, Macau b UMacau Research Institute, Zhuhai, Guangdong, China article info Article history: Received 25 April 2017 Received in revised form 16 July 2017 Accepted 31 July 2017 Keywords: Column supported embankment Axisymmetric model Load transfer Modulus ratio Stress ratio abstract In this study, a simplified axisymmetric model is built to simulate a column supported embankment sys- tem. The model is based on a cylindrical unit cell that contains one column with the surrounding soil and a layer of overlying embankment fill. The deformation of the column with the surrounding soil is simu- lated using a deformed shape function. The embankment fill is divided into an inner cylinder and an outer hollow cylinder to simulate the soil arching effect. The stress continuity and volume deformation conti- nuity are applied to combine the behavior of the embankment fill and that of the column-reinforced foundation together. A semi-analytical solution is obtained, and it is verified using a finite element anal- ysis and a case study. After that, parametric studies are put forward to evaluate the load transfer mech- anism within the embankment fill, the shear stress at the interface between the column and the surrounding soil, and the vertical stress distribution within the column. The influences of the column modulus, the spacing between columns, the height of the embankment fill, and the length of the column on the soil arching effect are investigated and discussed. It is concluded that when the column modulus becomes larger, the stress ratio between the column and the surrounding soil increases correspondingly. The height of equal settlement plane is close to the net spacing between columns, but it changes slightly with a change in the column modulus. Ó 2017 Elsevier Ltd. All rights reserved. 1. Introduction Column reinforcement under an embankment system is a type of technique to strengthen the foundation soil and has been proven efficient in enhancing the bearing capacity [1–10], reducing the settlement of the embankment [11–19] and increasing the consol- idation rate [20–22]. Some researchers adopted geosynthetic rein- forcements [23–31] to make the load transfer more efficient within the embankment fill. Because of the imbedded columns, the stiff- ness of the foundation is no longer uniform. As the modulus of the column is much larger than that of the surrounding soil, it will result in a larger settlement in the foundation soil [32,33] in con- trast to that of the column under the uniform load of the embank- ment fill. This differential settlement in the column-reinforced foundation that causes part of the embankment fill above the foun- dation soil has a tendency to move downward. This movement triggers shear resistance within the embankment fill, which trans- fers the load of the embankment fill endured by the surrounding foundation soil onto the column. Consequently, the stress increases on the column but decreases on the surrounding foundation soil. This is the soil arching effect. Hewlett and Randolph [34] used an arch to describe the soil arching effect in a two-dimensional model and used a dome in a three-dimensional model. Based on Hewlett and Randolph’s theory [34], Low et al. [35] included cap beams and a layer of geotextile to investigate the influences on the load trans- fer efficiency. Kempfert et al. [36] proposed the multi shell arching theory, and it was adopted in EBGEO [37] and recommended in BS8006 [38] as an alternative design method. Van Eekelen et al. [39] proposed a novel analytical model using concentric arches based on the limit-state equilibrium theory to describe the arching effect. Zhou et al. [6] investigated the group effect of soil arching using the finite element method. It can be found that these studies mainly concentrated on the soil arching effect and neglected the deformation of the columns. These theories are suitable for rigid piles made of concrete. However, with regard to some types of col- umns with a relatively small stiffness, such as stone columns and soil-cement mixed columns, the deformation cannot be negligible. The differential settlement between columns and the surrounding http://dx.doi.org/10.1016/j.compgeo.2017.07.027 0266-352X/Ó 2017 Elsevier Ltd. All rights reserved. ⇑ Corresponding author at: Department of Civil and Environmental Engineering, Faculty of Science and Technology, University of Macau, Avenida da Universidade, Taipa, Macau. E-mail addresses: z.l.s0319@gmail.com (L.-S. Zhao), hannahzhou@umac.mo (W.-H. Zhou), kvyuen@umac.mo (K.-V. Yuen). Computers and Geotechnics 92 (2017) 96–107 Contents lists available at ScienceDirect Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo