Page 311 - Numerical Analysis and Modelling in Geomechanics

292 ANALYSIS AND DESIGN OF PILE GROUPS
Treatment of multi-layered soil profiles
Mindlin’s solution is strictly applicable to homogeneous soil conditions.
However, in practice, this limitation is not strictly adhered to, and the influence
of soil non-homogeneity is often approximated using some averaging of the soil
moduli. PGROUPN handles multi-layered soils according to the averaging
procedure first examined by Poulos (1979) and widely accepted in practice
(Chow, 1986a, 1987; Poulos, 1989, 1990; Xu and Poulos, 2000): in the
evaluation of the influence of one loaded element on another, the value of the
soil modulus is taken as the mean of the values at the two elements. This
procedure is adequate in most practical cases but becomes less accurate if large
differences in soil modulus exist between adjacent elements or if a soil layer is
overlain by a much stiffer layer (Poulos, 1989).

Finite soil layer

Mindlin’s solution has been used to obtain approximate solutions for a layer of
finite thickness by employing the Steinbrenner approximation (Steinbrenner,
1934) to allow for the effect of the underlying rigid base in reducing the soil
displacements (Poulos andDavis, 1980; Poulos, 1989).

Pile domain
If the piles are assumed to act as simple beam-columns which are fixed at their
heads to the pile cap, the displacements and tractions over each element can be
related to each other via the elementary beam theory, yielding:

(10.2)

where {u } are the pile displacements, {t } are the pile tractions, {B} are the pile
p
p
displacements due to unit boundary displacements and rotations of the pile cap,
and [G ] is a matrix of coefficients obtained from the elementary (Bernoulli-
p
Euler) beam theory.
Solution of the system
The soil and pile equations (10.1) and (10.2) may be coupled via compatibility
and equilibrium constraints at the pile-soil interface. Thus, by specifying unit
boundary conditions, i.e. unit values of vertical displacement, horizontal
displacement and rotation of the pile cap, these equations are solved, thereby
leading to the distribution of stresses, loads and moments in the piles for any
loading condition.