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A practical method for the non-linear analysis of piled rafts
Une méthode d'analyse pratique pour déterminer la réponse non linéaire des fondations mixtes de
type radier sur pieux
Basile F.
Geomarc Ltd, London, United Kingdom
ABSTRACT: The paper describes a practical analysis method for determining the response of piled rafts. The key feature of the
method lies in its capability to provide a non-linear complete boundary element solution of the soil continuum, while retaining a
computationally efficient code. The validity of the proposed analysis is demonstrated through comparison with alternative numerical
solutions and field measurements. Examples are given to demonstrate the importance of considering soil nonlinearity effects in piled
rafts (given the relatively high load level at which the piles operate), thereby leading to more realistic predictions of the raft and pile
response. The negligible computational costs make the analysis suitable not only for the design of piled rafts supporting high rise
buildings (generally based on complex and expensive 3D FEM or FDM analyses) but also for that of bridges and ordinary buildings.
RÉSUMÉ: Cet article décrit une méthode d'analyse pratique pour déterminer la réponse des fondations mixtes de type radier sur
pieux. La principale caractéristique de la méthode réside dans sa capacité à fournir une solution non linéaire de type « Boundary
Element » du continuum sol, tout en conservant un code de calcul efficace. La validité de l'analyse proposée est démontrée par
comparaison avec d'autres solutions numériques et des mesures
in situ
. Des exemples sont donnés pour démontrer l'importance de la
prise en compte de la non-linéarité du sol dans l’analyse des radiers sur pieux, ce qui conduit à des prévisions plus réalistes de réponse
du radier et pieu. Les coûts négligeables de calcul rendent l'analyse appropriée non seulement pour la conception des radiers sur pieux
supportant des immeubles de grande hauteur (basé sur des analyses 3D en éléments ou différences finies, complexes et coûteuses),
mais aussi pour celle des bâtiments ordinaires et des ponts.
KEYWORDS: CPRF, piled raft, pile group, non-linear, numerical analysis
1 INTRODUCTION
In conventional foundation design, it is assumed that the applied
load is carried either by the raft or by the piles, considering the
safety factors in each case. In recent years, an increasing
number of structures have been founded on Combined Pile-Raft
Foundations (CPRFs), an attractive foundation system which
allows the load to be shared between the raft and the piles,
thereby offering a more economical solution. In the design of
piled rafts, a sufficient safety against geotechnical failure of the
overall
pile-raft system has to be achieved, while the piles may
potentially be used up to their ultimate geotechnical capacity.
Contrary to traditional pile foundation design, no proof for the
ultimate capacity of each individual pile is necessary
(Katzenbach 2012). Given the high load level at which the piles
operate, consideration of soil nonlinearity effects is essential,
and ignoring this aspect can lead to inaccurate predictions of the
deformations and structural actions within the system.
Due to the 3D nature of the problem and the complexity of
soil-structure interaction effects, calculation procedures for
piled rafts are based on numerical analyses, ranging from
simplified Winkler approaches (e.g. “plate on springs” methods)
to rigorous 3D finite element (FEM) or finite difference (FDM)
solutions using available packages. While Winkler models
suffer from some restrictions mainly related to their semi-
empirical nature and fundamental limitations (e.g. disregard of
soil continuity), finite element and finite difference solutions
retain the essential aspects of interaction through the soil
continuum, thereby providing a more realistic representation of
the problem. However, even though 3D FEM and FDM
analyses are powerful numerical tools which allow complex
geometries and soil behaviour to be modelled, such analyses are
burdened by the high computational cost and specialist expertise
needed for their execution, particularly if non-linear soil
behaviour is to be considered. This aspect restricts their
practical application in routine design, where multiple load
cases need to be examined and where the pile number,
properties and location may have to be altered several times in
order to obtain an optimized solution.
In an attempt to provide a practical tool for the designer, the
paper describes an efficient analysis method for determining the
response of piled rafts. The main feature of the approach lies in
its capability to provide a non-linear complete boundary
element (BEM) solution of the soil continuum (i.e. the
simultaneous influence of all the pile and raft elements is
considered), while retaining a computationally efficient code.
Validity of the proposed analysis is assessed through
comparison with alternative numerical solutions and a published
case history. Examples are given to highlight the significance of
considering soil nonlinearity effects, thereby leading to more
realistic predictions of the raft and pile response.
2 METHOD OF ANALYSIS
The safe and economic design of piled rafts requires non-linear
methods of analysis which have the capacity of simulating all
relevant interactions between the fondation elements and the
subsoil, specifically (1) pile-soil-interaction (i.e. single pile
response including shaft-base interaction), (2) pile-pile-
interaction (i.e. group effects), (3) raft-soil-interaction, and (4)
pile-raft interaction (Katzenbach 2012).
The proposed method is an extension of the BEM
formulation employed in the pile-group program PGROUPN
(Basile 2003) and widely used in pile design through the
software Repute (Bond and Basile 2010). The originality of the
approach lies in its ability to provide a complete BEM analysis
of the soil continuum (in which all four of the above
interactions are modelled), while incurring negligible
computational costs. Indeed, compared to FEM or FDM
analyses, BEM provides a complete problem solution in terms
of boundary values only, specifically at the raft-pile-soil
interface. This leads to a drastic reduction in unknowns to be
solved for, thereby resulting in substantial savings in computing
time and data preparation effort. This feature is particularly
significant for three-dimensional problems such as piled rafts
