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2nd
International Conference on Tunnel Boring Machines in Difficult Grounds (TBM DiGs Istanbul) Istanbul, 16–18 November 2016
DESIGN CHARTS FOR ESTIMATING FACE STAND-UP TIME IN SOFT
GROUND TUNNELLING
R. Schuerch1, R. Poggiati
1, P. Maspoli
1, G. Anagnostou
1
1ETH Zurich, Switzerland. Email: [email protected]
ABSTRACT: Under unstable face conditions, inspections and maintenance work in the working chamber of
EPBs or slurry shields have to be carried out under compressed air conditions. As hyperbaric interventions
generally present operational disadvantages, the question often arises as to whether the face may be stable at
least for the limited period of an intervention. In fact, if the ground exhibits a medium or low permeability,
then the face – even if unstable in the long-term – may be stable for a practically significant period of time.
Estimations of the stand-time of the face (i.e. the time lapsing from the beginning of the standstill until
collapse) are thus important for assessing the feasibility of atmospheric interventions in the working
chamber. Short-term stability can be traced back to excavation-induced negative excess pore pressures.
Stability deteriorates over time due to excess pore pressure dissipation during the consolidation process.
Instability occurs earlier or later depending on the permeability of the ground. In an on-going research
project, the phenomenon of delayed failure was investigated in laboratory tests under controlled conditions;
the experimental results can be reasonably reproduced using hydraulic-mechanical coupled spatial FEM
analyses. Based upon a suite of such analyses, dimensionless design charts were worked out, which allow the
stand-up time of a tunnel face to be estimated for a wide range of ground parameters and overburdens of
between one and four tunnel diameters.
KEYWORDS: Delayed failure; Stand-up time; Tunnel face; Design charts; Numerical modelling
1. INTRODUCTION
The response of water-bearing medium-low permeability ground to tunnel excavation is time dependent. The
time-dependency is due to a transient seepage flow process that is triggered by excavation and develops
slowly over the course of time. Experience shows that the short-term behaviour of the ground is more
favourable than the long-term one: the deformations increase with time, so the tunnel face may be stable
initially and fail only after some time. The time over which the tunnel face remains stable is called the stand-
up time.
This paper investigates the time dependency of the tunnel face stability assuming that all time effects are
due to consolidation rather than creep. This assumption is reasonable for shallow tunnels crossing water-
bearing soils. In the problem under analysis, the unsupported tunnel face remains stable under the undrained
conditions prevailing after excavation, but collapses before reaching the drained conditions prevailing at a
steady state.
The assessment of stand-up time is important from a financial standpoint for both mechanized and
conventional tunnelling through weak water-bearing ground, as a long stand-up time removes the need for
face support or ground improvement work during standstills, thus saving time and money, while short stand-
up times require hyperbaric interventions or the implementation of costly and time-consuming auxiliary
measures (Anagnostou, 2014).
The response of the ground to excavation under transient conditions is inherently governed by the strong
interaction between seepage flow and soil deformation. For this reason, face collapse cannot be investigated
by traditional limit equilibrium models (such as that of Anagnostou and Kovári, 1994), but only through
fully coupled hydraulic-mechanical stress analyses. Due to the complexity of the problem, few works have
addressed this topic: Höfle et al. (2009) investigated the stability of the unsupported face during on-going
tunnel excavation, while Ng and Lee (2002) estimated the necessary face reinforcement as a function of the
consolidation time. Only Schuerch and Anagnostou (2013a, 2013b, 2016) and Callari (2015) focused on the
stand-up time of the tunnel face. There is also relatively little research work on the similar problems of
delayed failure in slopes and excavations (e.g. Holt and Griffiths, 1992, Potts et al., 1997, Vaughan and
Walbancke, 1973).
We investigated delayed failure by starting from fundamental experimental and numerical research into
the speed of shear band propagation that considered relatively simple geotechnical problems (see Section 2).
These investigations served to validate the numerical models and computational assumptions. From this
point, we proceeded to study the mechanism of delayed face failure and the stand-up time of shallow tunnels
by means of coupled numerical stress-seepage flow analyses (Sections 3 and 4). Based on the results of a
comprehensive parametric study, we worked out design nomograms (Section 5) that show the stand-up time
for a wide range of geotechnical conditions (soil properties, depth of cover, height of water table). These
nomograms will assist tunnel engineers in their decision-making (see Section 6 for an application example).
2. FUNDAMENTAL RESEARCH
The goal of the research was to develop a computational method for estimating stand-up time, and thus to
improve construction safety and economy.
First, the basic possibility of reproducing delayed failure computationally was investigated by means of
fully coupled hydraulic-mechanical continuum-mechanical simulations. The ground was modelled as an
isotropic, linearly elastic and perfectly plastic material obeying the Mohr-Coulomb (MC) yield criterion. The
reasons for selecting the MC model were: it is widely used in engineering practice and there is considerable
practical experience with its parameters. Emphasis was placed on the numerical manifestation of failure, on
the role of the plastic dilatancy and, finally, on the influence of the spatial discretization. In order to achieve
this goal, two simple plane strain problem were considered: an underwater vertical excavation and a bi-axial
test (Schuerch and Anagnostou, 2015a and b, respectively).
The numerical study showed that, under the frequently-made simplifying assumption of a constant
positive dilation angle, coupled analyses inevitably lead to a constant deformation rate at failure, while
failure is commonly associated with accelerating displacements. Models that allow for shearing under
constant volume lead to accelerating displacements, but inherently exhibit numerical stability problems close
to the failure state, because no solution satisfies the two balance equations (Schuerch and Anagnostou,
2015a). Moreover, the assumption of non-associated plastic flow leads to a dependency between the stand-up
time and the coarseness of the mesh: the finer the mesh, the lower the stand-up time (Schuerch and
Anagnostou, 2015b). The mesh-dependency of the stand-up time is mainly due to the structural softening
that occurs even in a perfectly plastic material if the flow rule is non-associated. In numerical simulations,
the shear strains become localized in a band which is about 1–2 finite elements thick.
Figure 1. Experimental research into the phenomenon of delayed failure: (a) drum centrifuge with assembled model and, (b), deformed model at failure.
ω
(b)(a)
The coarser the finite element mesh, the thicker will be the numerically-predicted shear band, the smaller the
shear strains, the less pronounced the structural softening and the longer the predicted stand-up time. For
very coarse finite element meshes (which practically prevent structural softening) the stand-up time tends to
an upper limit. Vice-versa, very fine meshes allow for considerable structural softening (up to that
corresponding to purely plastic shearing) and the stand-up time tends to a shorter limit. These two limits in
the stand-up time can be determined analytically in the case of relatively simple problems. Finally, the
numerical simulations show that for sufficiently fine spatial discretization, the stand-up time depends almost
linearly on the element size (see Fig. 2 as example). This finding is valuable from the practical viewpoint, as
it allows stand-up time to be determined by performing a few computations with relatively fine meshes and
their results to be extrapolated to the mesh size that corresponds to the expected, grain-size-dependent
thickness of the shear band (practically zero considering the dimensions of typical geotechnical structures).
The experimental part of the fundamental research was aimed at observing delayed failure under
controlled conditions and consists of uniaxial loading tests and centrifuge tests (the latter simulate the
excavation of an underwater vertical cut in over-consolidated clay; Fig. 1). The experimental results were
interpreted also numerically, using material constants which were determined by means of laboratory tests or
based upon theoretical considerations, independently from the delayed failure tests ("class A" model
validation). The interpretation shows that the MC model with isochoric plastic flow provides a conservative
estimate of the stand-up time (particularly when extrapolating the results to the thickness of the shear band;
see Fig. 2 as example). The reason is that it does not account for the plastic volumetric strains accompanying
shearing, which temporarily perpetuate negative excess pore pressures, thus delaying failure.
Figure 2. Theoretical research into the phenomenon of delayed failure: stand-up time as a function of mesh size (s) on an example of underwater vertical excavation (centrifuge modelling). The two sets of ground
parameters considered in the numerical analysis correspond to lower and upper bound of the material cohesion, respectively.
0
25
50
75
100
125
150
175
200
225
250
0.00 0.20 0.40 0.60 0.80 1.00 1.20
t s[d]
s [m]
MC (c' = 9 kPa)
MC (c' = 7 kPa)
very fine mesh
(s/H = 3%)
fine mesh
(s/H = 7%)
coarse mesh
(s/H = 14%)
Experimental range
linear extrapolation
to a zero mesh size
11 d9 d
H
3. COMPUTATIONAL MODEL
The numerical analysis is carried out using the FE program Abaqus (Dassault Systèmes, 2012). Figure 3
shows a typical numerical model. The ground is discretized by 8-node brick elements (C3D8P). The element
size e varies from 0.5 m (close to the tunnel face) to 6 m (at the model boundary).
The water table is taken equal to the elevation of the ground surface (Hw = H). No-flow conditions are
imposed at the tunnel wall (which is true for a practically impervious lining) and at the symmetry plane. A
mixed boundary condition is imposed at the tunnel face, ensuring that pore water can flow out of the ground,
but cannot enter into the ground (a no-flow condition in the case of a negative boundary pore pressure). At
the far field boundaries, the potential is fixed to its initial value. This assumption is adequate provided that
the groundwater recharge from the surface suffices for maintaining the water table at its initial elevation in
spite of the drainage action of the tunnel. The tunnel lining is simulated in a simplified way by fixing all
nodal displacements at the tunnel wall.
The initial vertical stress corresponds to the overburden pressure at each point. The analyses have been
performed for two lateral pressure coefficient values (K0 = 0.5 and 1.0) corresponding to different degrees of
consolidation of the soil.
The Abaqus subroutine UMAT, which performs the integration of the elasto-plastic incremental
equations of the MC model, is according to Clausen et al. (2005). Table 1 summarizes the parameters
considered in the analysis.
The stability of the tunnel face under transient conditions is investigated by means of a numerical
analysis of the consolidation process starting with a simulation of the excavation as an undrained process.
This simple simulation procedure is reasonable in the case of an advance rate that is fast compared to ground
permeability so that the conditions prevailing around the face during advance remain undrained.
4. STAND-UP TIME OF THE TUNNEL FACE
In order to improve our understanding of the basic mechanism of delayed failure, we first discuss the results
for a specific example (Fig. 4 and 5).
The determination of stand-up time requires an evaluation of the time-development of several parameters
simultaneously: the displacements, the volumetric strains and the effective stresses at certain control points
(cf. Schuerch and Anagnostou 2012, 2015). This is because the stability of the numerical solution
deteriorates close to failure, thus making an identification of the time point of failure difficult. For the sake
of simplicity, we will show only the evolution over time of the plastic zone (Fig. 4a) and of the
displacements at points A, C and D (Fig. 4b).
Table 1. Assumed material constant
Saturated unit weight [kN/m3] 20
Lateral pressure coefficient K0 [-] 0.5, 1.0
Unit weight of water w [kN/m3] 10
Seepage flow parameters
Permeability k [m/s] 10-7
Water compressibility cw [MPa] 0
Parameters for linearly elastic, perfectly plastic material
Young’s modulus E' [MPa] 20
Poisson’s ratio [-] 0.3
Cohesion c' [MPa] 5–40
Friction angle ' [°] 15, 25, 35
Dilation angle ψ' [°] 0
Figure 3. Typical Numerical model.
Under undrained conditions (constant water content), the excavation causes plastic yielding of the ground
ahead of the tunnel face (line "0+" in Fig. 5b), accompanied by very small displacements toward the tunnel
face (Fig. 4b). Over time, the displacements increase and the plastic zone progressively expands towards the
ground surface. After approximately 11.3 hours the displacements increase rapidly (note that displacements
larger than 0.5–1 m violate the small strain and small displacement assumptions, and are included in Fig. 4b
only for the sake of completeness). The rapid evolution of the displacements indicates that the system is
approaching the ultimate state. Figure 4 shows that the displacements accelerate rapidly when the plastic
zone reaches the ground surface. The kinematics of the unstable zone agree well with the failure mechanisms
assumed in limit equilibrium models (cf., e.g., Anagnostou and Kovári, 1994). All of these observations
indicate that the stand-up time here amounts to about 11.3 hours.
As the mechanism underlying time-dependency is the dissipation of the excess pore pressures generated
by the undrained excavation, an analysis of their distribution may be illustrative. Figure 5 shows the
distribution of pore pressure and horizontal effective stress along a horizontal line ahead of the tunnel face at
several time points. The undrained excavation induces negative excess pore pressures ahead of the tunnel
face (line "t = 0+" in Fig. 5a), causing the axial effective stress ’x (Fig. 5b) to be compressive (which is
favourable for stability) in spite of the excavation-induced stress relief in the axial direction. During the
consolidation process, the negative excess pore pressures dissipate and consequently the effective stresses
and the shear resistance of the ground decrease. Once the plastic zone reaches the soil surface, further stress
redistribution is no longer possible.
We discuss next the influence of cohesion on the stand-up time, all the other parameters being kept the
same as in the previous example. As can be seen from Figure 6, the sensitivity of the stand-up time to
cohesion is remarkable: the tunnel face would collapse practically immediately after undrained excavation if
the cohesion is equal to 5 kPa, but would remain stable even in the long term (i.e. under drained conditions)
if the cohesion is higher than about 37 kPa. A critical cohesion of 37 kPa agrees well with the value
predicted by the method of slices assuming drained conditions (Perazzelli et al., 2014).
H = 10 m
D = 10 m
30 m
35 m
20 m
30 m
H = 20 m
D = 10 m
30 m
46 m
40 m
30 mH
= 1D
H= 2
D
60 m
40 m40 m
H = 40 m
D = 10 m
40 m
H= 4
D
Figure 4. (a) Contour of the plastic zone at different time increments and displacement vectors (not scaled) close to the ultimate state of points A, B, C and D and, (b), evolution of the displacements (ux, uz) at points
A, C, and D over time (the dashed vertical line crossing the time axis at t = ts = 11.3 h corresponds nearly to the ultimate state).
It should be noted that if the cohesion is higher than about 20 kPa, then tensile stresses develop in the ground
ahead of the tunnel face before the plastic zone reaches the soil surface. The occurrence of tensile stresses is
due to the gradient of the pore pressure field, which approaches a steady state distribution during the
consolidation process (Fig 5a) and is associated with seepage forces that are directed towards the face. The
tensile stresses are statically admissible only if the ground exhibits tensile strength, which presupposes the
presence of cementation bonds between the grains. Otherwise, tensile failure would occur in the form of
progressive raveling of the ground at the tunnel face. In the present example, tensile stresses start to develop
after about 10 hours. The computational prediction of over 10 hours of stand-up time ignores such local
instabilities.
Ground surface
t [h] =
7.7
5.3
2.3
A
B
492 mm
D
C
0+
153 mm
334 mm
z
x [m]
158 mm11.3
0+
5 10
Elastic region
Elasticregion
11.3
H = D
D = 10 m
c' = 20 kPa
' = 25
K0 = 1.0
Other parameters
according to Table 1
(a)
-4
-3
-2
-1
0
1
2
3
4
0 5 10
ux
[m]
t [h]
Nearly ultimatestate uA,x
uD,x
uC,x
uA,z
uC,z
uD,z
(b)
+
uz[m
]
Figure 5. Spatial distributions along the x-axis, (a), of the pore pressure p and, (b), of the effective horizontal stress 'x.
Figure 7.13.Stand-up time of the tunnel face as a function of the cohesion c' for a ground with (solid line) and without (dashed line) tensile strength.
5. DESIGN CHARTS
Figures 7 and 8 show the results of a parametric study into the effects of soil strength (c', '), the coefficient
of horizontal stress K0 and depth of cover (H/D) on the stand-up time of an unsupported tunnel face.
For dimensional reasons and due to the structure of the equations underlying consolidation theory, a
dimensionless stand-up time Ts can be defined as tskE/('D2), which is a function of the normalized cohesion
c'/('D) and of the other model parameters (', K0, , , H/D, Hw/H, w/'). Note that the stand-up time is
inversely proportional to soil permeability: if the permeability or Young’s modulus is higher by a factor of
ten, the stand-up time will be ten times shorter.
Figure 7 is based upon the finite element computations with the finer mesh (s/D = 0.05) and partially
revises the results presented in Schuerch et al. (2016) because it considers additional computations. On the
one hand, the design diagrams of Figure 7 overestimate the stand-up time because they are obtained for a
mesh size which leads to a shear band thickness larger than the expected one. On the other hand, they
-150
-100
-50
0
50
100
150
200
0 5 10 15
POR 0+ t1
POR 2.25 h t2
POR 11.3 h t5
POR Last t6
-230
-180
-130
-80
-30
0 5 10 15
' x
[kP
a]
p[k
Pa
]
x [m]
t = 0+
0+ < t < ts (Dt = 2.5 h)
t = ts
steady state
distribution
(a) (b) x [m]
x
z
Tunnel face
0
10
20
30
40
50
60
70
5 10 15 20 25 30 35 40
occurrenceof tensile stress
t s[h
]
c' [kPa]
H=Hw= 10 m
D = 10 m
’ = 25
K0 = 1
k = 10-7 m/s
E = 20 Mpa
= 20 kN/m3
underestimate the stand-up time because they do not consider the plastic dilation, which, as explained in
Section 2, delays the occurrence of failure. As these two effects are opposite, the design diagrams of Figure 7
give a stand-up time which may be close to the real one.
Figure 8 was obtained by a linear extrapolation of the numerical results for 0.5 m and 1.0 m to an
element size of zero (as exemplary shown by Fig. 2). The extrapolation has been performed only for results
exhibiting an almost linear relationship between stand-up time and mesh size. The design nomograms of
Figure 8 give a lower limit for the stand-up time – thus representing a conservative version of the charts of
Figure 7 – because they do not consider the plastic dilation.
Generally, considering the uncertainties related to ground parameters (particularly permeability), the
influence of mesh size on the stand-up time (illustrated by the differences between Figs. 7 and 8) is not
relevant from a practical engineering point of view. Indeed, the mesh-dependency is relevant only if the
strength is close to the cohesion that is required for face stability under drained conditions.
6. APPLICATION EXAMPLE
In order to illustrate the utility of the design diagrams, let us consider the following example, based upon the
construction of the tunnel of Line 3 of the Athens Metro. The tunnel is under construction with an EPB
machine and runs beneath the south-west of the city. From an operational standpoint, it is advantageous to
carry out inspection and/or maintenance of the cutterhead under atmospheric conditions. For this reason, the
stability of the unsupported tunnel face is investigated in specific tunnel locations. The ground at tunnel
elevation consists of weak Lower Athens Schists, overlayed by a layer of the more competent Upper Athens
Schists. The water table is located at the ground surface (Fig. 9a).
The design nomograms are applied making the conservative assumption of homogenous ground, with the
mechanical and hydraulic properties of the particularly weak Lower Athens Schists. Two models are
considered: one extending up to the boundary between the two geological units (Fig. 9b) and, one extending
up to the ground surface (Fig. 9c). For the parameter set given in Figure 9 (normalized cohesion c'/('D) =
0.24, friction angle ' = 25°), the dimensionless stand-up time obtained with Figure 7 is equal to 0.05 –
0.075, while tensile stresses would start developing at 0.065 – 0.1. With a simple transformation taking into
account the permeability of the ground k, the Young's modulus E, the submerged unit weight of the ground ' and the tunnel diameter D, the stand-up time amounts to 10 – 15 hours. The design diagrams of Figure 8
provide a stand-up time of 2 – 8 hours. This period is sufficient for depressurizing and emptying the working
chamber and carrying out routine inspection and maintenance work.
The field experience agreed well with the computational predictions: after 6 hours of work inside the
excavation chamber under atmospheric conditions the first indications of instability were observed (in the
form of some ravelling in the upper part of the tunnel face). As a consequence the excavation chamber was
evacuated and re-pressurized again.
This simple application example shows the usefulness of using the design diagrams: they assist
operational decision-making – in the present example related to the feasibility of manned entries in the
cutterhead chamber under atmospheric conditions.
Figure 9. (a) Geological profile; (b, c) simplified models assumed for an estimation of the stand-up time from the design nomograms.
considered tunnel
location
D = 9.5 mTBM
9.5 m
9.5 m Upper Athens Schists
Lower Athens Schists
' = 13 kN/m3
K0 = 0.5
E = 160 MPa
c' = 30 kPa
' = 21
k = 10-8 m/s
(a) (b) (c)
Surface deposits
Figure 7. Dimensionless diagrams for determining the stand-up time of the tunnel face (= 0°, = 0.3, Hw / H = 1, w / '=1) obtained for an element size of 0.05 D.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
' = 25
15
H=Hw=4D
D
K0 = 0.5
H/Hw = 1
w/’ = 1
= 0
= 0.3
H/D = 4
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.400.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
' = 35 25
15
H=Hw=D
D
K0 = 1
H/Hw = 1
w/’ = 1
= 0
= 0.3
H/D = 1
occurrenceof
tensile stress
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
' = 35 25 15
H=Hw=2D
D
K0 = 1
H/Hw = 1
w/’ = 1
= 0
= 0.3
H/D = 2
occurrenceof
tensile stress
' = 35 25 15
H=Hw=D
D
K0 = 0.5
H/Hw = 1
w/’ = 1
= 0
= 0.3
H/D = 1
occurrenceof
tensile stress
' = 35 25
15
H=Hw=2D
D
K0 = 0.5
H/Hw = 1
w/’ = 1
= 0
= 0.3
H/D = 2
occurrenceof
tensile stress
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
' = 25
15
H=Hw=4D
D
K0 = 1
H/Hw = 1
w/’ = 1
= 0
= 0.3
H/D = 4
occurrenceof
tensile stress
occurrenceof
tensile stress
2-
stk
E
D
c -γ D
(f)
c -γ D
c -γ D
(a)
2-
stk
E
D
c -γ D
(c)
c -γ D
(b)
2-
stk
E
D
(d)
2-
stk
E
D
c -γ D
(e)
H/D = 1
H/D = 2
H/D = 4
K0 = 1 K0 = 0.5
2-
stk
E
D
2-
stk
E
D
Figure 8. Dimensionless diagrams for the determination of the stand-up time of the tunnel face obtained based upon linear extrapolation to a zero element size (= 0°, = 0.3, Hw / H = 1, w / '=1).
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.400.00
0.05
0.10
0.15
0.20
0.25
0.30
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.400.00
0.04
0.08
0.12
0.16
0.20
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
0.00
0.03
0.06
0.09
0.12
0.15
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.400.00
0.01
0.02
0.03
0.04
0.05
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
2-
stk
E
D
c -γ D
' = 25
15
H=Hw=4D
D
K0 = 0.5
H/Hw = 1
w/’ = 1
= 0
= 0.3
H/D = 4
(f)
c -γ D
2-
stk
E
D
c -γ D
' = 35
25 15
(a)
H=Hw=D
D
K0 = 1
H/Hw = 1
w/’ = 1
= 0
= 0.3
H/D = 1
2-
stk
E
D
c -γ D
' = 35 25
15
(c)
H=Hw=2D
D
K0 = 1
H/Hw = 1
w/’ = 1
= 0
= 0.3
H/D = 2
2-
stk
E
D
c -γ D
' = 35 25 15
(b)
H=Hw=D
D
K0 = 0.5
H/Hw = 1
w/’ = 1
= 0
= 0.3
H/D = 1
2-
stk
E
D
' = 35 25
15
(d)
H=Hw=2D
D
K0 = 0.5
H/Hw = 1
w/’ = 1
= 0
= 0.3
H/D = 2
2-
stk
E
D
c -γ D
' = 25
15
H=Hw=4D
D
K0 = 1
H/Hw = 1
w/’ = 1
= 0
= 0.3
H/D = 4
(e)
H/D = 1
H/D = 2
H/D = 4
K0 = 1 K0 = 0.5
7. THE INFLUENCE OF SUPPORT PRESSURE ON STAND-UP TIME
The design diagrams apply to an unsupported tunnel face, i.e. to the worst case with respect to stability. The
application of a moderate air pressure, compensating the in situ hydrostatic pressure only in part, is often a
simple matter operationally, however, particularly considering that short stand-up times are disadvantageous,
too.
Figure 10 shows the influence of the air pressure on the stand-up time for the example of a 20 m deep
tunnel with a diameter of 10 m. The air pressure is taken into account computationally by applying the
pressure as a uniform total stress and imposing it as a hydraulic boundary condition at the tunnel face.
The effect of a moderate air pressure is remarkable: in a hyperbaric intervention under just 1 bar (40% of
the in situ hydrostatic pressure), the stand-up time would be twice as long as in the case of an atmospheric
intervention.
8. CONCLUSIONS
Experience shows that tunnel faces may be stable in the short term, but collapse after a certain time period.
The stand-up time of the tunnel face is important in engineering practice, especially in medium- and low-
permeability water-bearing ground. Theoretical models are able to explain the phenomenon of delayed
failure, showing that instability occurs more or less rapidly depending on the permeability, stiffness and
shear strength of the ground, as well as on the coefficient of lateral pressure, and they provide useful
indications regarding the stand-up time. On the basis of a parametric study, we worked out design diagrams
allowing the stand-up time to be estimated for a given geotechnical situation, thus assisting on-site decision-
making. In view of the underlying simplifying assumptions (e.g. homogenous ground and undrained
conditions up to the beginning of the stand-still period) their use presupposes a measure of engineering
judgment. Due to the uncertainties related to the computation method and to the heterogeneity of the ground
(concerning both structure and material parameters), a sufficiently high safety factor should be applied to the
estimated stand-up time, and the face behaviour should be monitored during standstills in order to detect any
onset of instability (e.g. cracks, extrusion, increasing water inflows, ravelling) in good time. In the case of
unsatisfactory ground behaviour, re-pressurization of the excavation chamber (mechanized tunnelling) or
reinforcement of the face (conventional tunnelling) will be required. In this context, we showed that even a
moderate support pressure (0.5 to 1 bar) can increase the stand-up time of the tunnel face considerably.
Figure 10. Stand-up time of the tunnel face as a function of the applied support pressure.
0
5
10
15
20
25
30
35
40
45
50
0 25 50 75 100
ps [kPa]
t s[h
]
H=Hw=2D
D =10 m
' = 25
c' = 20 kPa
K0 = 1
k = 10-7 m/s
E = 20 MPa
= 20 kN/m3
ps
Partial compensation of the water
pressure pw= ps
9. ACKNOWLEDGEMENTS
This paper evolved within the framework of the research project "Tunnel face stability and tunneling induced
settlements under transient conditions". The support given to this project by the Swiss Tunnelling Society
(STS) and the Federal Road Office of Switzerland (FEDRO) is greatly appreciated.
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