3395
An undrained upper bound solution for the face stability of tunnels reinforced by
micropiles
Une solution en limite supérieure non drainée pour la stabilité du front de tunnels renforcés par
micropieux
Pinyol N.M.
Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE).
Department of Geotechnical Engineering and Geo-Sciences. Universitat Politècnica de Catalunya (UPC)
Alonso E.E.
Department of Geotechnical Engineering and Geo-Sciences. Universitat Politècnica de Catalunya (UPC)
ABSTRACT: Tunnel in difficult soils may require procedures to prevent tunnel face failures. Face stabilization can be achieved by
the installation of some structural elements. This paper presents an analysis of face stability of shallow tunnels in undrained soils
reinforced by an umbrella of subhorizontal micropiles. Upper bound solutions for two dimensional plane strain conditions are given
including the effect of micropiles. The micropile umbrella is embedded in the soil and supported on the tunnel lining. The
kinematically admissible collapse mechanism defined to calculate the upper bound solution includes the action provided by a
subhorizontal micropile at limiting conditions. The solutions are given in practical dimensionless charts which are useful to quantify
easily the effect of the umbrella of micropiles. The plots provide a simple procedure to design the umbrella. The most relevant
properties defining the umbrella are grouped into a single dimensionless coefficient which includes the yielding conditions and the
geometry of the micropiles as well as the distance between them.
RÉSUMÉ : Les tunnels dans les sols difficiles peuvent nécessiter des procédés pour prévenir les ruptures du front du tunnel. La
stabilisation du front peut être réalisée par l’installation de certains éléments structurels. Cet article présente une analyse de la stabilité
du front dans des tunnels peu profonds en conditions non drainées renforcés par un parapluie de micropieux subhorizontaux. Des
solutions de la limite supérieure pour des conditions bidimensionnelles de déformation plane sont présentées, y compris l’effet des
micropieux. Le parapluie de micropieux est intégré dans le sol et soutenu sur le revêtement du tunnel. Le mécanisme de rupture
cinématiquement admissible défini pour calculer la solution de la limite supérieure comprend la réponse prévue par un micropieu
subhorizontal dans des conditions limites. Les solutions sont données dans des graphiques pratiques et sans dimensions qui
fournissent une procédure simple de concevoir le parapluie. Les propriétés les plus pertinents qui définissent le parapluie sont
regroupées en un seul coefficient sans dimension qui inclut les conditions de plastification et de la géométrie des micropieux, ainsi
que la distance qui les sépare.
KEYWORDS: Tunnel, face stability, micropiles, upper bound, plasticity, undrained strength.
1 INTRODUCTION
Tunnel in difficult soils may require procedures to prevent
tunnel face failures. In tunnel excavated by means of boring
machines, a pressure can be applied against the face to
counteract water and earth pressure. Several publications
provide procedures to calculate the pressure required for
stability. Well known solutions given initially by Davis et al.
(1980) offer practical dimensionless charts for shallow tunnels
in cohesive materials based on plasticity theorems (upper and
lower bound solutions). This contribution was followed by
several authors that presented similar solutions for frictional
materials (Leca and Dormieux 1990) or improved solutions by
using limit equilibrium, finite difference and finite element
methods (Lyamin and Sloan 2002a,b, Augarde et al. 2003,
Vermeer et al. 2002, Klar et al. 2007, among others).
Another calculation approach is to use Limit Equilibrium
techniques (Anagnostou and Kovari 1996). They provide their
results in terms of “bearing capacity” expressions. Finite
Element and Distinct Element methods have been used
extensively to examine face stability, in most cases under three
dimensional conditions (Vermeer
et al
. 2002, Galli
et al
. 2003,
Melis and Medina 2005). Among them, Vermeer
et al.
(2002)
determined failure conditions of the face by means of a “
c
,
reduction method” and provided three dimensional solutions for
the drained case.
Face stabilization can also be achieved by the installation of
some structural elements (bolts distributed in the front, concrete
prevaults and umbrellas of micropiles). Several analysis of
tunnel face stability taking into account the effect of a prevault
and a reinforcement by bolts have been published (Peila et al.
1996, Wong et al. 2000, Yoo and Shin 2003, Lignola et al.
2008, 2010). However, limited attention has been paid to the
reinforcement of tunnel faces by micropiles.
This paper presents a stability analysis of tunnel faces
including an umbrella of sub-horizontal micropiles. The
micropiles are considered as beams subjected to the kinematic
motion imposed by the assumed failure mechanism. The
limiting resistance of the supporting beams is first addressed.
The failure mechanism imposes a displacement pattern on the
beam, which reacts applying a critical combination of normal
and shear forces on the boundary of the sliding body. These
limiting supporting forces are calculated by assuming a Von
Mises yield criterion for the micropile material. Then, they are
introduced into the general minimization process associated
with the upper bound formulation. Stability conditions are
described in terms of dimensionless parameters and plotted in
ready to use design charts. In particular, a dimensionless
Micropile Coefficient, which includes all the relevant design
parameters of the umbrella, could be isolated and plotted in
terms of undrained soil strength and tunnel geometry.
2 UPPER BOUND SOLUTION INCLUDING
SUBHORIZONTAL MICROPILES
2.1 Collapse mechanism
Consider the plane strain shallow circular tunnel of diameter
D
,
having a cover depth
C
, represented in Figure 1. The soil around
the tunnel is characterized by its unit weight (
) and its
undrained strength (
c
u
). A vertical stress,
S
, is applied on the
soil surface. In order to prevent a potential failure of the front, a
