A recently proposed meshless method, which is called the radial basis POINT INTERPOLATION method (RBPIM), is used for the mechanical analysis of reinforced soils. The media of reinforced soil is divided into three parts: soil, reinforcement and interface layer. The displacement field in each part is constructed by POINT INTERPOLATION. A code has been developed based on RBPIM and the validity of this code has been investigated by solving some examples at the end of the paper.

Sustainability studies, from the POINT of view of regional identification with the potential of failure in the soil, and from the POINT of view of designing the new engineering structures, are considered as important issues in geotechnical engineering and have always been a significant part of the references in this field. Subject is dedicated. In the meantime, instability analysis in classical geotechnical problems such as the back of the retaining wall, bearing capacity of foundation and slopes and landslides with a progressive failure mechanism, is considered as a challenging topic in this discussion. These issues are in the category of issues with large displacements and have always attracted the attention of many scholars in recent years. With advances in computer technology and computational techniques, numerical methods such as finite difference, finite element, and boundary components have been widely employed in analyzing engineering issues. In the meantime, the finite element method, due to the ability of that method to control issues with geometry and complex conditions and modeling the behavior of soil shape change, has increased significantly compared to other numerical methods. In conventional analyzes of soil slopes failure, resistance parameters are assumed to be stable even in large strains without change. However, during the rupture, soil resistance exhibits maximum and residual amounts, and its strength increases prematurely by increasing the plastic strain. In addition to changing soil resistance parameters in the progressive mechanism, the non-uniform nature of the soil also causes spatial variations of these parameters. Therefore, geotechnical systems should be considered in terms of the uncertainty of soil parameters values uncertainly using the concepts of statistics and probabilities. The simulation of a progressive failure is definite or non-deterministic only by applying numerical techniques such as finite element method that are able to simulate the development of deviant plastic strain. Although the finite element method is widely used in the analysis of sustainability issues, however, this approach is based on problems that are essentially related to gridding. In this research, a radial POINT INTERPOLATION method in combination with a random field was used to model the spatial variations of soil resistance properties and slope instability analysis. In order to consider the progressive failure of soil, elastoplastic method has been developed with the Coulomb Moore's behavioral model for applying strain softness. For probabilistic analysis, the random field is also used to determine the cohesion parameters and the friction angle as well as the plastic strain threshold based on their mean values and standard deviation. In order to investigate the application of the POINT INTERPOLATION method with randomized radial functions, a geotechnical earthwork with definite and non-deterministic geometry has been analyzed and its reliability coefficients has been investigated. Based on the analysis of the progressive failure modeling, it is concluded that the actual failure of the soil and the occurrence of continuous displacements occur simultaneously with the formation of a progressive mechanism of soil degradation and the arrival of the slipping path to the ground. In the following, probabilistic distribution functions of the coefficient of reliability were determined by probabilistic analysis and the production of random fields, and then the statistical parameters are calculated.

This work studies (2D) Sobolev equations by pseudospectral meshless radial POINT INTERPOLATION (PSMRPI). The Sobolev equations which are arisen in the uid ow penetrating rocks, soils, or di erent viscous media do not have an exact solution except in some special cases. Approximation of highorder derivatives through operational matrices is possible. It is proved that the method is convergent and unconditionally stable. Also, the important results for the Sobolev equation are validated for the purpose of showing the ability of this technique.

Accurate irrigation planning needs soil water content monitoring. Determining of soil properties, such as soil water content, that show spatial variability,  in form of a global quantity and neglecting its spatial variability, is not adequate for site-specific-management. In this study, the estimation and mapping of soil water content, in field capacity (FC) and permanent wilting POINT (PWP), were compared by global mean, inverse distance weighting (IDW) and ordinary kriging INTERPOLATION methods. Results showed that a clear spatial structure could be identified for both FC and PWP. Estimation accuracy increase for using of global mean, IDW and ordinary kriging methods respectively. These results suggest that kriged maps can be used for irrigation planning programs because as more accurate INTERPOLATION from water content at FC and PWP.

In the current work, we implement the meshless local radial POINT INTERPOLATION (MLRPI) method to find numerical solution of one-dimensional linear telegraph equations with variable coefficients. The MLRPI method, as a meshless technique, does not require any background integration cells and all integrations are carried out locally over small quadrature domains of regular shapes, such as lines in one dimensions, circles or squares in two dimensions and spheres or cubes in three dimensions. Weak form formulation of the discretized equations has been constructed on local subdomains, hence the domain and boundary integrals in the weak form methods can easily be evaluated over the regularly shaped subdomains by some numerical quadratures. Radial basis functions augmented with monomials are used in to create shape functions. These shape functions have delta function property. Also the time derivatives is eliminated by using two-step finite differences approximation. Two illustrative numerical examples are given to show the stability and accuracy of the present method.