Finite element analysis of footings and MAT foundation

Abstract

This thesis deals with the analysis of footings and mat foundation by finite element method. The foundation mats are modelled with thick plate elements which include 4 noded bilinear element, 8 noded serendipity quadratic element and heterosis element. All are based on Mindlin's assumptions. Isoparametric, formulation is considered in the study. In numerical computation Gauss integration rule together with reduced integration technique is employed. The soil under the foundation is considered as Winkler medium and subgrade reaction (kg) concept is used. ----" -.- The node springs are computed by using either the contributing area method or the shape function method at element level and added to appropriate diagonal terms of element stiffness matrix. Similady, the vertical as well as the rotational stiffness of piles ai'e added to element stiffness matrix in case of pile foundation. Equation solving is performed using the powerful' frontal solution technique. The convergence of solution is checked by using both displacement and residual force norm criteria. In Winkler foundation using a constant kg on a rectangular uniformly loaded flexible base will produce constant settlements which is not in agreement with the Boussinesq solution., To make the displacements comparable with Boussinesq solution, soil zoning suggested by Bowles is considered in the study and its effect on the numerical results are studied. The effects of mat rigidity on the behaviour of foundation are also considered. Finite element program developed in the study is, mainly for foundation analysis, but it is capable to analyse slab problems of any type. The appropriate order of quadrature for 'different Mindlin plate elements have been examined. Moreover, a smoothing technique to calculate stress resultants of nodes from the stress resultants at Gauss points is developed. Higher order elements used are found to be quite efficient in the analysis of slab and foundation problems. For most of the cases convergence is found within 2 to 3 iterations. For eccentric footing where soil footing separation occurs about 10 iterations are required. Due to bilinear behaviour the performance of 4 noded element under concentrated load is found to be unsatisfactory.