Example (7.3): Circular foundation subjected to eccentric loading
Introduction
The simplest model for determination of the contact pressure
under the foundation assumes a planar distribution of contact pressure on the bottom of the
foundation (statically determined). In which the resultant of soil reactions coincides with the
resultant of applied loads. If all contact pressures are compression, the foundation system
will be considered as linear and the contact pressures in this case is given
directly.
If the foundation subjects to big eccentricity, there will
be negative contact pressures on some nodes on the foundation. Since the soil cannot resist
negative stress, the foundation system becomes nonlinear and a resolution must be carried out to
find the nonlinear contact pressures.
The nonlinear analysis of foundation for the simple
assumption model has been treated by many authors since a long time, where several analytical and
graphical methods were available for the solution of this problem.
Pohl (1918) presented
a table to determine the maximum corner pressure
max qo
for arbitrary positions of the resultant
N.
Hülsdünker
(1964) developed a diagram using the numerical
values of this table from
Pohl (1918) to determine the
maximum corner pressure max qo.
For one corner detached footing, the closed form formulae cannot be
used. Therefore, Pohl
(1918) and
Mohr (1918) proposed a
method to estimate the neutral axis through the trial and error. Besides tables and diagrams,
Graßhoff
(1978) introduced also influence line charts can
be used to determine the contact pressure ordinates.
Peck/ Hanson/ Thornburn
(1974) indicated a trial and error method to
obtain the neutral axis position for rectangular footing subjected to moments about
both axes. Jarquio/ Jarquio
(1983) proposed a direct method of proportioning a rectangular
footing area subjected to biaxial bending. Irles/
Irles (1994) presented an analytical
solution for rectangular footings with biaxial bending, which will lead to obtain explicit solutions for
the corner pressures and neutral axis location.
The determination of the actual contact area and the maximum
corner pressure max qo
under eccentric loaded foundation with irregular shape is very
important. For Tshape foundation that is loaded eccentrically in the symmetry axis,
Kirschbaum
(1970) derived formulae to determine the maximum corner pressure
max qo.
For some foundation areas with polygonal boundaries,
Dimitrov (1977) gave
formulae to determine the foundation kern and corner pressure
max qo. For the same purpose,
Miklos
(1964) developed diagrams. For general cases of
foundation,
Opladen (1958)
presented graphical procedure.
Most of the analytical methods used to determine the contact
area and corner pressures for eccentric loaded foundations are focused on regular
foundations where irregular foundations can be analyzed only by graphical procedures. In this paper, an
iteration procedure is presented to deal with nonlinear analysis of foundations for simple
assumption model. The procedure can be applied for any arbitrary foundation shape and is suitable
for computer programs. The following section describes this procedure.
Description of the problem
Another example is considered to show the applicability of
nonlinear analysis of foundations using the program ELPLA for simple assumption model to
different foundation types. The results of nonlinear analysis for a circular raft calculated
by Teng
(1962) are compared with those obtained by the program
ELPLA.
A circular raft of radius
r
= 5 [m] is considered as shown in the Figure.
The raft carries an eccentric load of
N = 2000 [kN]. The position of the
resultant N
is defined by the ordinate
e.
