Page 310 - Numerical Analysis and Modelling in Geomechanics

F.BASILE 291

Table 10.2 Features of group behaviour and their effect on corner loads

Note
× indicates capability: (1)=using elastic-plastic soil model

Burghignoli and Desideri (1995). The analysis involves discretisation of only
the pile-soil interface into a number of cylindrical elements, while the base is
represented by a circular (disc) element. The method employs a substructuring
technique in which the piles and the surrounding soil are considered separately
and then compatibility and equilibrium conditions are imposed at the interface. A
description of the basic theoretical formulation of the PGROUPN analysis has
been presented elsewhere (Basile, 1999) and hence only a brief description will
be given here. However, the additional features that have recently been
introduced will be described in some detail.

Soil domain
The boundary element method involves the integration of an appropriate
elementary singular solution for the soil medium over the surface of the problem
domain, i.e. the pile-soil interface. With reference to the present problem, the
well-established solution of Mindlin (1936) for a point load within a
homogeneous, isotropic elastic half-space has been adopted, yielding:

(10.1)

where {u } are the soil displacements, {t } are the soil tractions and [G ] is the
s
s
s
flexibility matrix obtained from Mindlin’s solution. The singular part of the [G ]
s
matrix is calculated via analytical integration of the Mindlin functions. This is a
significant advance over previous work (e.g. PGROUP) where these have been
integrated numerically, since these singular integrals require considerable
computational resources.