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Equilibrium models for arching in basal reinforced piled embankments
Modèles d’équilibre par effet voute pour l'amélioration des sols de fondation par inclusions rigides
Eekelen van S.J.M.
Deltares, Unit Geo-Engineering and Delft University of Technology, Netherlands
Bezuijen A.
Ghent University, Belgium and Deltares, Netherlands
ABSTRACT: Several analytical models are available for describing arching in basal reinforced piled embankments using
geosynthetics. Some of them are limit state equilibrium models. Two of them are frequently applied in Europe: the model of Zaeske
(2001), the model of Hewlett and Randolph (1988), but both models have only been described very briefly in the English language.
This paper considers these two models along with another, new one: the Concentric Arches Model (Van Eekelen et al. 2013b). The
paper gives a graphical presentation of the models and summarizes and discusses them.
RÉSUMÉ : Plusieurs modèles analytiques sont disponibles pour décrire la distribution en arcs des forces dans une l'amélioration des
sols de fondation par inclusions rigides et géosynthétique. Parmi eux, il y a des modèles d'équilibre aux états-limites. Deux d'entre eux
sont fréquemment appliquées en Europe : le modèle de Zaeske (2001), le modèle de Hewlett et Randolph (1988, mais les deux
modèles ont seulement été décrits très brièvement dans la langue anglaise. Le présent article examine ces deux modèles et les compare
avec notre nouveau modèle: le Modèle Arches Concentriques (Van Eekelen et al. 2013b). L’article donne une représentation
graphique des modèles qui sont résumés et discutés.
KEYWORDS: arching, piled embankments, geosynthetic reinforcement, basal reinforced load transfer platforms
MOTS-CLES: effet voutes, inclusion rigide, renforcement géosynthétique, plateforme de transfert de charge
1 DESIGN OF BASAL REINFORCED PILED
EMBANKMENTS
Many analytical design models for the design of piled
embankments distinguish two calculation steps. Step 1 is the
arching behaviour in the fill. This “arching step” divides the
total vertical load into two parts: load part A, and the ‘rest load’
(B+C in Figure 1). Load part A, also called the ‘arching’, is the
part of the load that is transferred to the piles directly.
Calculation step 2 describes the load-deflection behaviour of
the geosynthetic reinforcement (GR) (see Figure 1). In this
calculation step, the ‘rest load’ is applied to the GR strip
between each two adjacent piles, and the GR strain is
calculated. An implicit result of step 2 is that the ‘rest load’ is
divided into a load part B, which goes through the GR to the
piles, and a part C, resting on the subsoil, as indicated in Figure
1.
geometry
properties
load
strain ε
step 1
“arching”
load part A
load part B+C
step 2
“membrane”
B
A
A
C C soft
subsoil
B+C
support from subsoil (C)
z
GR strip
Figure 1. Calculating the geosynthetic reinforcement (GR) strain
comprises two calculation steps.
This paper focuses on calculation step 1 only and thus on the
determination of the load distribution in the load transfer
platform. The two most interesting results of the arching step
are:
1. The calculated value for the arching A (kN/pile)
2. The load distribution of B+C (kN/pile)
Van Eekelen et al. (2012a, b and 2013a) showed with
experiments, numerical calculations and field measurements
that load B+C is concentrated on the GR strips between each
two adjacent piles, and that the load distribution on these strips
approaches the inversed triangular shape, as shown in Figure 1
(right hand side of the figure). The two most applied models in
Europe (Zaeske 2001 and Hewlett and Randolph 1988) are
summarized, analysed and discussed in this paper.
Zaeske (2001), between several other researchers, showed
the great influence of the application of a sufficient stiff GR in a
piled embankment. The concentration of load on GR strips is
only found for GR basal reinforced piled embankments, not for
piled embankments without GR. Therefore, it is necessary to
make a distinction between arching models for piled
embankment with and without GR. This paper focuses on GR
reinforced piled embankments only.
2 EQUILIBRIUM MODELS DESCRIBING ARCHING
In equilibrium models, an imaginary limit-state stress-arch is
assumed to appear above the void between stiff elements. In the
3D situation these stiff elements are piles, in the 2D situation
they are walls. The pressure on the void (GR) is calculated by
considering the equilibrium of the arch. In most models, the
arch has a thickness.
The model of Hewlett and Randolph (1988, see Figure 2) is
adopted in the French ASIRI guideline (2012) and suggested in
BS8006 (2010) as an alternative for the originally first empirical
model in BS8006. The other frequently applied equilibrium
model is the model of Zaeske (2001, also described in
Kempfert, 2004). See Figure 3. This model is adopted in the
German EBGEO (2010) and the Dutch CUR226 (2010), and is
hereafter called EBGEO. These two models are of great
importance.
