Time Dependent Analysis of Tunnels Using The Finite Element Method
Engineering and Technology Journal,
2009, Volume 27, Issue 1, Pages 127-151
AbstractThe analyses of tunnels in clay were carried out taking into consideration two
great important and effective categories, the time independent and time dependent. Time
independent behaviours are used to represent the excavation stage while time dependent
analyses are used to represent the behaviour of the unlined tunnel after a long time.
The finite element analyses were carried out using the linear elastic model for the
concrete liner while elasto-plastic and modified Cam clay model for the soil. The
excavation has been used together with transient effects through a fully coupled Biot
formulation. All these models and the excavation technique together with Biot
consolidation are implemented into finite element computer program named "Modf-
CRISP" developed for the purpose of these analyses.
In this paper, the basic problem represents the proposed "Baghdad metro line"
which consists of two routes of (32 km) long and 36 stations is analyzed. The tunnel is
circular in cross section with a (5.9) m outer diameter and (0.45) m of concrete lining
thickness. Eight-node isoparametric elements are used to model the soil and concrete
lining. Four-node element is used for pore water pressure.
Two kinds of analyses are carried out:
a- Using elastic-plastic constitutive model for all soil layers.
b- Using modified Cam clay model (MCC) for the first soil layer (upper layer) and
elastic-plastic Mohr Coulomb for the other two layers.
The movements of the soil around the tunnel at the end of excavation at typical
points (crown, spring line and the invert) are calculated. The results indicate that there is
an inward movement at the crown and this movement is restricted to four and a half
tunnel diameters. A limited movement can be noticed at spring line which reaches
0.05% of tunnel diameter, while there is a heave at the region below the invert, which
reaches its maximum value of about 0.14% of the diameter and is also restricted to a
region extending to (1.5) diameters.
It was found that the maximum consolidation settlement above the tunnel is about
three times that at the end of excavation. The settlement trough extends only to (5)
tunnel diameters using consolidation analysis while it is extended to (12) tunnel
diameters using undrained analysis.
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