Application of Random Radial Point Interpolation Method to Foundations Bearing Capacity Considering Progressive Failure

In conventional analyzes of foundations failure, strengh parameters are assumed constant. However, during the failure, soil resistance exhibits maximum and residual amounts, and its strength decreases prematurely by increasing the plastic strain. In addition to change soil strengh 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 purpose of this study is to investigate foundations in meshless method. In this article, radial point interpolation method (RPIM), a meshless method is proposed for simulation of soil foundation. Difficulties of methods related to mesh are solved by using this method. A code has been developed based on this method and some examples are solved for analyzing the code. In this research, a RPIM in combination with a random field was used to model the spatial variations of soil strengh properties and foundation bearing capacity analysis. For probabilistic analysis, random field is also used to determine the cohesion and the friction angle as well as the dilation angle based on their mean values and standard deviation. In order to investigate the application of the point interpolation method with randomized radial functions, a foundation with definite geometry has been analyzed deterministic and probabilistic and its safety factor 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 failure and the arrival of the slipping path to the ground. In the following, probabilistic distribution functions of the safety factor were determined by probabilistic analysis and the production of random fields, and then the statistical parameters are calculated.