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.
