آنالیز غیر خطی در مطالعه فونداسیون گرید سطحی Nonlinearity analysis in studying shallow grid foundation

1. Introduction The accuracy of the finite element analysis is still a concerned point although it starts from 30 years ago. This accuracy was classified by Bathe in the nonlinear analysis especially in four classes; (1) small deformation in which; large displacements and rotation occurs but with small strain, (2) large deformation in which; large displacements, rotation, and strain occurs, (3) material nonlinearity, and (4) boundary nonlinearities such as contact and friction [14]. All these classes were widely studied by different techniques one of them was by M. Harnau et al. [9], who defined the large deformation contact analysis by the augmented Lagrangian method through studding structural finite ‘‘Solid-Shell” elements, and studied comparison of the contact algorithms used especially for problems in sheet metal forming [9]. Y. Hu and M.F. Randolph performed a numerical method for large deformation problems of soil [13], referred to as Remeshing and Interpolation Technique with Small Strain model (RITSS). Their method was used in pipeline and foundation penetration analyses. The RITSS method is based on a standard small strain algorithm, but with frequent remeshing, They also defined how error estimation and H-adaptive mesh generation techniques can be incorporated into the RITSS approach to reach the accuracy of large deformation analyses of foundations but with optimal meshes to minimize computational times [12,13]. Also, Changxin Wang and John P. Carter defined long deformation analysis by using the Arbitrary LagrangianEulerain (ALE) method which developed by Ghosh and Kikuchi, (1991), though studying the failure mechanism of a horizontally layered cohesive soil under the vertically loaded rigid strip and circular footings [17]. The aim of this paper is to discuss the effect of simulating a real soil foundation problem by deferent analysis types whether in linear or nonlinear classifications to reach the really and more accurate stress-strain soil behaviors. As the grid foundation is a special type of shallow foundation, in which the grid shapes has the great effect in transferring the concentrated loads applied on its interactions and load paths, the second aim of this study was generated. It is maintaining that, the loading techniques and the geometry of any foundation are responsible of assigning the required analysis degree. The theory of interfering foundations was first suggested by Das and Larbi-cherif (1983), where the effect of interference of shear zones on the bearing capacity of footings investigated and limited to parallel strip or rectangular foundations, the concepts of these experiments could be used to investigate any cross shape or grid foundation to explain the soil stresses beneath this foundations and evaluate the soil bearing which depends on the distance between the foundations. Ghazavi and Hadiani concerned with the foundation geometry during evaluate the ultimate bearing capacity of multiedge ‘‘Cross-shape, H-shape and T-shape” foundation through an experimental laboratory tests. They found that the bearing capacity of multi-edge foundation are generally greater and have a better performance than that of square shaped foundation with the same width [7], because of the interference of shear zones under the collected parts increases the shear resistance for the soil.