DESIGN CHARTS FOR ESTIMATING FACE STAND-UP TIME IN SOFT ... · DESIGN CHARTS FOR ESTIMATING FACE STAND-UP TIME IN SOFT GROUND TUNNELLING R. Schuerch1, R. Poggiati1, P. Maspoli1 ...

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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