Elasto-plastic analysis of reinforced soils using mesh-free method

In this paper the application of the mesh-free method (MFM) for the elasto-plastic analysis of reinforced soils is studied for the first time. The applied mesh-free method is called the radial point interpolation method (RPIM). In MFM, unlike the finite element method (FEM), there is no need of mesh in the traditional sense, and the shape functions are based on nodes. In the present study the reinforced soil is divided into three separate parts of soil, reinforcements, and interface layers. The displacement field in each part is constructed by RPIM. The final system of equations is derived by the substitution of the displacement field into the weak form of the governing equation. The elasto-plastic behaviors of soil, reinforcements, and interface layers are considered. There is also the ability of slippage modeling between the soil and reinforcement. Based on the derived equations a computer code has been developed and its validity investigated by solving some examples at the end of the paper. The use of fabric or polymer grid reinforcing material to improve the strength and stability of geotechnical structures is increasing. Generally, the investigation of the behavior of reinforced soil structures through field observation or laboratory modeling is expensive and time consuming. So it is necessary to develop numerical solutions which may be used to predict the load–deformation characteristics of reinforced soil structures. The most popular method for the numerical analysis of reinforced soils is the finite element method. Although FEM is widely used, there are some deficiencies such as the discon-tinuity of stresses on element boundaries, low accuracy at large deformation analysis or the weakness of the method in the two dimensional modeling of thin media (i.e. reinforcement). The mentioned shortcomings are mainly related to mesh definition. Therefore the authors have been encouraged to apply a new family of numerical methods, independent of mesh, for the analysis of reinforced soils. These new families of numerical methods are globally coined as mesh-free or meshless methods. MFM were developed by Lucy [1] who introduced smoothed particle hydrodynamics (SPH) for modeling astrophysical phenomena. Libersky and Petschek [2] extended this method to solve the solid mechanics problem. Nayroles et al. [3] extended a new branch of MFM by using a basis function and a weight function to form a local approximation based on a set of nodes. Belytschko et al. [4] improved this method by introducing the moving least square approximation and called …